Proyecto B. Índice de bondad de ajuste geométrico para datos simbólicos de tipo intervalo.
Dylan Benavides - CeNAT.
2025-04-21
1 Librerías.
## ##
## Attaching package: 'RSDA'## The following objects are masked from 'package:stats':
##
## cor, sd, var##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Linking to GEOS 3.7.2, GDAL 3.0.4, PROJ 6.3.2; sf_use_s2() is TRUE##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
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## filter## The following object is masked from 'package:graphics':
##
## layout2 Ejemplo 1. Datos simulados, modelo lineal.
n=100
x1.lower <- round(runif(n,0,2),2)
x1.upper <- x1.lower + round(runif(n,1,2))
x2.lower <- round(runif(n,0,2),2)
x2.upper <- x2.lower + round(runif(n,1,2))
x3.lower <- round(runif(n,0,2),2)
x3.upper <- x3.lower + round(runif(n,1,2))
x1.centers <- (x1.lower+x1.upper)/2
x2.centers <- (x2.lower+x2.upper)/2
x3.centers <- (x3.lower+x3.upper)/2
x1.ranks <- (x1.upper-x1.lower)/2
x2.ranks <- (x2.upper-x2.lower)/2
x3.ranks <- (x3.upper-x3.lower)/2
y.centers <- 0.6*x1.centers + 0.3*x2.centers + 0.1*x3.centers
y.ranks <- 0.6*x1.ranks + 0.3*x2.ranks + 0.1*x3.ranks
y.lower <- y.centers - y.ranks
y.upper <- y.centers + y.ranks
tabla <- data.frame(x1.lower,x1.upper,x2.lower,x2.upper,x3.lower,x3.upper,y.lower,y.upper, x1.centers, x1.ranks,x2.centers,x2.ranks,x3.centers,x3.ranks, y.centers, y.ranks)
#Gráficamente
library(patchwork)
# Rectángulos (x1, y)
p1 <- ggplot(tabla, aes(xmin = x1.lower, xmax = x1.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "skyblue", color = "black", alpha = 0.4) +
geom_point(aes(x = x1.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x1, y)", x = "x1", y = "y") +
theme_minimal()
# (x2, y)
p2 <- ggplot(tabla, aes(xmin = x2.lower, xmax = x2.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "palegreen", color = "black", alpha = 0.4) +
geom_point(aes(x = x2.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x2, y)", x = "x2", y = "y") +
theme_minimal()
# (x3, y)
p3 <- ggplot(tabla, aes(xmin = x3.lower, xmax = x3.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "salmon", color = "black", alpha = 0.4) +
geom_point(aes(x = x3.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x3, y)", x = "x3", y = "y") +
theme_minimal()
p1
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3
3 Para la variable \(x_{1}\).
geom_indicesc <- indice1$results[[1]]$geom_indices
geom_indicescmenosr <- indice2$results[[1]]$geom_indices
geom_indicescmasr <- indice3$results[[1]]$geom_indices
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr1, geom_indicescmasr1)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmenosr1$alpha, geom_indicescmasr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.006403124 -6.118289e-06
## [2,] 0.011000000 2.696153e-05
## [3,] 0.026500000 1.066538e-04
## [4,] 0.027856777 1.564911e-04
## [5,] 0.028792360 1.858687e-04
## [6,] 0.030500000 2.594634e-04
## [7,] 0.030675723 3.246862e-04
## [8,] 0.030805844 4.292464e-04
## [9,] 0.031764760 6.722323e-04
## [10,] 0.032649655 9.877870e-04
## [11,] 0.035032128 1.095374e-03
## [12,] 0.036619667 1.159084e-03
## [13,] 0.037696154 1.311225e-03
## [14,] 0.038160844 1.412498e-03
## [15,] 0.040012498 1.756081e-03
## [16,] 0.040311289 1.782774e-03
## [17,] 0.040816663 1.829525e-03
## [18,] 0.042201896 2.065869e-03
## [19,] 0.042216703 2.617354e-03
## [20,] 0.042252219 2.848080e-03
## [21,] 0.042426407 3.087585e-03
## [22,] 0.042438190 3.395552e-03
## [23,] 0.042898135 3.649410e-03
## [24,] 0.043139309 3.853019e-03
## [25,] 0.043660623 4.298264e-03
## [26,] 0.044821870 4.840319e-03
## [27,] 0.045069391 5.260976e-03
## [28,] 0.046446205 6.087293e-03
## [29,] 0.046960089 6.574999e-03
## [30,] 0.047087684 7.373194e-03
## [31,] 0.047563116 7.762183e-03
## [32,] 0.047762433 7.908817e-03
## [33,] 0.048383882 8.360825e-03
## [34,] 0.050022495 9.365393e-03
## [35,] 0.050159745 1.041492e-02
## [36,] 0.050358713 1.115034e-02
## [37,] 0.050990195 1.197852e-02
## [38,] 0.051662365 1.307496e-02
## [39,] 0.052354560 1.390031e-02
## [40,] 0.052430907 1.397356e-02
## [41,] 0.052680642 1.388489e-02
## [42,] 0.052841745 1.402522e-02
## [43,] 0.053667961 1.419416e-02
## [44,] 0.053851648 1.495577e-02
## [45,] 0.054120237 1.520881e-02
## [46,] 0.054600824 1.538695e-02
## [47,] 0.054644304 1.481873e-02
## [48,] 0.055020451 1.475735e-02
## [49,] 0.055056789 1.487447e-02
## [50,] 0.055145263 1.515439e-02
## [51,] 0.055454937 1.516320e-02
## [52,] 0.055509008 1.517786e-02
## [53,] 0.055832338 1.515976e-02
## [54,] 0.055901699 1.630065e-02
## [55,] 0.056189412 1.773492e-02
## [56,] 0.056293872 1.778004e-02
## [57,] 0.056703175 1.877597e-02
## [58,] 0.056797887 1.900861e-02
## [59,] 0.057008771 1.992377e-02
## [60,] 0.057116110 2.040007e-02
## [61,] 0.057404268 2.157914e-02
## [62,] 0.057870545 2.280508e-02
## [63,] 0.057974132 2.289241e-02
## [64,] 0.058148517 2.266528e-02
## [65,] 0.059002119 2.317638e-02
## [66,] 0.059052942 2.322531e-02
## [67,] 0.059600755 2.441953e-02
## [68,] 0.060299254 2.458108e-02
## [69,] 0.060827625 2.476379e-02
## [70,] 0.060911822 2.575712e-02
## [71,] 0.061491869 2.630082e-02
## [72,] 0.061491869 2.630082e-02
## [73,] 0.062201286 2.666085e-02
## [74,] 0.062801274 2.677900e-02
## [75,] 0.063158531 2.649514e-02
## [76,] 0.063198101 2.680937e-02
## [77,] 0.063294945 2.702761e-02
## [78,] 0.063631753 2.763639e-02
## [79,] 0.063641574 2.763707e-02
## [80,] 0.063994140 2.803949e-02
## [81,] 0.064437955 2.914692e-02
## [82,] 0.064693508 2.934165e-02
## [83,] 0.064809336 2.943948e-02
## [84,] 0.065069194 2.950416e-02
## [85,] 0.065094163 2.956546e-02
## [86,] 0.065192024 3.098250e-02
## [87,] 0.066001894 3.140167e-02
## [88,] 0.066009469 3.140059e-02
## [89,] 0.066098411 3.138928e-02
## [90,] 0.066387122 3.161825e-02
## [91,] 0.066640828 3.225138e-02
## [92,] 0.066753277 3.321284e-02
## [93,] 0.067529623 3.378145e-02
## [94,] 0.067581432 3.470257e-02
## [95,] 0.067603624 3.473862e-02
## [96,] 0.068014704 3.539369e-02
## [97,] 0.068900290 3.624195e-02
## [98,] 0.069500000 3.652106e-02
## [99,] 0.070087445 3.678143e-02
## [100,] 0.070301138 3.816866e-02
## [101,] 0.072277244 3.856071e-02
## [102,] 0.072527581 3.862762e-02
## [103,] 0.072670489 3.968742e-02
## [104,] 0.073015409 4.051657e-02
## [105,] 0.073681748 4.167336e-02
## [106,] 0.074546965 4.184105e-02
## [107,] 0.074546965 4.184105e-02
## [108,] 0.075000000 4.154881e-02
## [109,] 0.075208045 4.131676e-02
## [110,] 0.075208045 4.479916e-02
## [111,] 0.075325958 4.475621e-02
## [112,] 0.075802375 4.583546e-02
## [113,] 0.076216796 4.631638e-02
## [114,] 0.076500000 4.665878e-02
## [115,] 0.076557168 4.627090e-02
## [116,] 0.076609399 4.632900e-02
## [117,] 0.077162167 4.701601e-02
## [118,] 0.077388630 4.817735e-02
## [119,] 0.077828337 5.002006e-02
## [120,] 0.078262379 5.251412e-02
## [121,] 0.078461774 5.251683e-02
## [122,] 0.078492038 5.192212e-02
## [123,] 0.078773409 5.107582e-02
## [124,] 0.079323704 5.123663e-02
## [125,] 0.079342612 5.007171e-02
## [126,] 0.079657078 5.006685e-02
## [127,] 0.080263628 5.087534e-02
## [128,] 0.080721744 5.230496e-02
## [129,] 0.081610355 5.408661e-02
## [130,] 0.081891697 5.668546e-02
## [131,] 0.082000000 5.783802e-02
## [132,] 0.082384768 6.186581e-02
## [133,] 0.082947272 6.230700e-02
## [134,] 0.083103851 6.231279e-02
## [135,] 0.083798866 6.187334e-02
## [136,] 0.083815273 6.186064e-02
## [137,] 0.084559151 6.120535e-02
## [138,] 0.084824819 6.109828e-02
## [139,] 0.085248167 6.130120e-02
## [140,] 0.085328776 6.033051e-02
## [141,] 0.085616879 6.027363e-02
## [142,] 0.085912746 6.184319e-02
## [143,] 0.086204698 6.198819e-02
## [144,] 0.086227896 6.072567e-02
## [145,] 0.086227896 6.072567e-02
## [146,] 0.086278618 6.037449e-02
## [147,] 0.086863399 6.160163e-02
## [148,] 0.086989942 6.069710e-02
## [149,] 0.087097646 6.090516e-02
## [150,] 0.087458562 6.121579e-02
## [151,] 0.088255311 6.153403e-02
## [152,] 0.089140339 6.236818e-02
## [153,] 0.089269256 6.254565e-02
## [154,] 0.090138782 6.488358e-02
## [155,] 0.090138782 6.488358e-02
## [156,] 0.091685604 6.770559e-02
## [157,] 0.093017471 6.971890e-02
## [158,] 0.093107465 6.687732e-02
## [159,] 0.093178592 6.698685e-02
## [160,] 0.093553461 6.841016e-02
## [161,] 0.095117033 6.872797e-02
## [162,] 0.095524866 6.808070e-02
## [163,] 0.096130120 6.772714e-02
## [164,] 0.097186676 6.798047e-02
## [165,] 0.097325485 7.048992e-02
## [166,] 0.097514102 7.512871e-02
## [167,] 0.098184775 7.825055e-02
## [168,] 0.098508883 8.072670e-02
## [169,] 0.099575348 8.452323e-02
## [170,] 0.100101199 8.504184e-02
## [171,] 0.100623059 8.470518e-02
## [172,] 0.100778222 8.396430e-02
## [173,] 0.101212647 8.441307e-02
## [174,] 0.102415819 8.519613e-02
## [175,] 0.103077641 8.547402e-02
## [176,] 0.103712343 8.499195e-02
## [177,] 0.104000000 8.439348e-02
## [178,] 0.105475116 8.431838e-02
## [179,] 0.105905618 8.524624e-02
## [180,] 0.105990566 8.547258e-02
## [181,] 0.107070071 8.763472e-02
## [182,] 0.107178589 9.090856e-02
## [183,] 0.108632408 9.795452e-02
## [184,] 0.108908218 1.025224e-01
## [185,] 0.110163515 1.052431e-01
## [186,] 0.110205490 1.045477e-01
## [187,] 0.110222502 1.030570e-01
## [188,] 0.110500000 9.958888e-02
## [189,] 0.110613064 9.978326e-02
## [190,] 0.111230616 1.015046e-01
## [191,] 0.111507847 1.052727e-01
## [192,] 0.112044634 1.079951e-01
## [193,] 0.112695386 1.113777e-01
## [194,] 0.112787411 1.118156e-01
## [195,] 0.113715654 1.128297e-01
## [196,] 0.114127122 1.134752e-01
## [197,] 0.114284732 1.135297e-01
## [198,] 0.114808536 1.149364e-01
## [199,] 0.115004348 1.158518e-01
## [200,] 0.115524889 1.171420e-01
## [201,] 0.115932092 1.162076e-01
## [202,] 0.116914499 1.187607e-01
## [203,] 0.117517020 1.205514e-01
## [204,] 0.118013770 1.206411e-01
## [205,] 0.118309974 1.175630e-01
## [206,] 0.118431415 1.160874e-01
## [207,] 0.119189974 1.155850e-01
## [208,] 0.120016666 1.169156e-01
## [209,] 0.120016666 1.169156e-01
## [210,] 0.120203993 1.183568e-01
## [211,] 0.120440857 1.222073e-01
## [212,] 0.120917327 1.245974e-01
## [213,] 0.120933866 1.246671e-01
## [214,] 0.121594613 1.270318e-01
## [215,] 0.121594613 1.270318e-01
## [216,] 0.121597697 1.253183e-01
## [217,] 0.122576507 1.253014e-01
## [218,] 0.122918672 1.244533e-01
## [219,] 0.123693169 1.241962e-01
## [220,] 0.123916302 1.241683e-01
## [221,] 0.124233651 1.292127e-01
## [222,] 0.125905719 1.298872e-01
## [223,] 0.126178445 1.287585e-01
## [224,] 0.126289350 1.272850e-01
## [225,] 0.126822711 1.272064e-01
## [226,] 0.127059041 1.268223e-01
## [227,] 0.127059041 1.255831e-01
## [228,] 0.127910125 1.242499e-01
## [229,] 0.128363741 1.240880e-01
## [230,] 0.128538905 1.242011e-01
## [231,] 0.130000000 1.239049e-01
## [232,] 0.130648383 1.232889e-01
## [233,] 0.130981869 1.228468e-01
## [234,] 0.131359240 1.215404e-01
## [235,] 0.133761915 1.219962e-01
## [236,] 0.133869339 1.226114e-01
## [237,] 0.134202273 1.227895e-01
## [238,] 0.134402381 1.232005e-01
## [239,] 0.134792433 1.216889e-01
## [240,] 0.134871235 1.214059e-01
## [241,] 0.135333846 1.204540e-01
## [242,] 0.135447407 1.176533e-01
## [243,] 0.136701317 1.165274e-01
## [244,] 0.139316187 1.161360e-01
## [245,] 0.140000893 1.154790e-01
## [246,] 0.140204315 1.138396e-01
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## [250,] 0.141223228 1.211557e-01
## [251,] 0.142538591 1.291563e-01
## [252,] 0.143461667 1.298753e-01
## [253,] 0.144779142 1.282546e-01
## [254,] 0.145455320 1.258019e-01
## [255,] 0.145627092 1.238630e-01
## [256,] 0.145723197 1.247209e-01
## [257,] 0.145880088 1.228512e-01
## [258,] 0.147678705 1.234052e-01
## [259,] 0.148141824 1.227834e-01
## [260,] 0.148291099 1.180555e-01
## [261,] 0.148846397 1.167079e-01
## [262,] 0.149495819 1.162115e-01
## [263,] 0.151792622 1.169389e-01
## [264,] 0.153733536 1.236024e-01
## [265,] 0.154155765 1.257370e-01
## [266,] 0.155724918 1.262382e-01
## [267,] 0.160078106 1.282938e-01
## [268,] 0.160920011 1.277422e-01
## [269,] 0.161721984 1.274226e-01
## [270,] 0.164924225 1.275728e-01
## [271,] 0.165075740 1.270568e-01
## [272,] 0.165822948 1.263050e-01
## [273,] 0.165847068 1.222050e-01
## [274,] 0.167039666 1.222707e-01
## [275,] 0.167377567 1.184289e-01
## [276,] 0.169189243 1.180886e-01
## [277,] 0.170472872 1.195615e-01
## [278,] 0.171026314 1.140779e-01
## [279,] 0.171354165 1.140657e-01
## [280,] 0.171421265 1.142153e-01
## [281,] 0.172046505 1.202375e-01
## [282,] 0.172154727 1.230008e-01
## [283,] 0.177545065 1.283057e-01
## [284,] 0.180017360 1.393743e-01
## [285,] 0.181176709 1.434686e-01
## [286,] 0.182608872 1.440862e-01
## [287,] 0.184361059 1.450162e-01
## [288,] 0.185326738 1.443107e-01
## [289,] 0.187235814 1.448591e-01
## [290,] 0.189423467 1.464074e-01
## [291,] 0.193124960 1.457265e-01
## [292,] 0.193287998 1.419268e-01
## [293,] 0.197689782 1.386892e-01
## [294,] 0.200124961 1.377101e-01
## [295,] 0.208583916 1.356015e-01
## [296,] 0.211733913 1.355028e-01
## [297,] 0.214683488 1.371308e-01
## [298,] 0.215195260 1.373521e-01
## [299,] 0.221317080 1.359459e-01
## [300,] 0.221472346 1.360027e-01
## [301,] 0.227705951 1.357827e-01
## [302,] 0.229907046 1.334352e-01
## [303,] 0.234534113 1.324864e-01
## [304,] 0.238227307 1.285400e-01
## [305,] 0.240881714 1.230406e-01
## [306,] 0.243507700 1.177407e-01
## [307,] 0.245538184 1.131470e-01
## [308,] 0.245728000 1.105467e-01
## [309,] 0.252666282 1.115192e-01
## [310,] 0.255141627 1.067688e-01
## [311,] 0.255970701 1.029059e-01
## [312,] 0.256048823 1.025725e-01
## [313,] 0.258677405 9.937900e-02
## [314,] 0.259108568 9.925250e-02
## [315,] 0.264756492 9.649525e-02
## [316,] 0.271463165 8.849575e-02
## [317,] 0.273507313 8.357715e-02
## [318,] 0.274200656 8.181765e-02
## [319,] 0.277477927 6.861526e-02
## [320,] 0.285273991 6.152571e-02
## [321,] 0.290924818 6.104174e-02
## [322,] 0.291686476 6.081232e-02
## [323,] 0.297793553 5.954309e-02
## [324,] 0.334570247 5.539550e-02
## [325,] 0.365815527 4.127402e-02
## [326,] 0.372013441 4.141517e-02
## [327,] 0.403886123 4.311658e-02
## [328,] 0.433159613 4.477267e-02
## [329,] 0.481923230 4.553141e-02
## [330,] 0.482566317 5.131291e-02
## [331,] 0.503791872 5.379601e-02
## [332,] 0.514796319 4.542341e-02
## [333,] 0.541742790 4.960164e-02
## [334,] 0.553754458 4.899256e-02
## [335,] 0.589091674 4.811889e-02
## [336,] 0.780688959 4.183992e-02
## [337,] 0.927340822 3.622333e-02
## [338,] 0.954564822 3.314736e-02
## [1] 0.000000e+00 1.239388e-07 1.777073e-06 1.989397e-06 2.163292e-06
## [6] 2.606362e-06 2.663417e-06 2.719271e-06 3.363886e-06 4.237974e-06
## [11] 6.847673e-06 8.687764e-06 1.009928e-05 1.075566e-05 1.400731e-05
## [16] 1.453999e-05 1.546458e-05 1.832629e-05 1.836505e-05 1.846620e-05
## [21] 1.900402e-05 1.904403e-05 2.072256e-05 2.165181e-05 2.389255e-05
## [26] 2.951335e-05 3.081556e-05 3.919663e-05 4.257542e-05 4.351620e-05
## [31] 4.720659e-05 4.878295e-05 5.397877e-05 6.932503e-05 7.075448e-05
## [36] 7.297304e-05 8.053726e-05 8.932586e-05 9.894758e-05 1.000144e-04
## [41] 1.034820e-04 1.057415e-04 1.174689e-04 1.202161e-04 1.243010e-04
## [46] 1.316958e-04 1.323401e-04 1.378910e-04 1.384315e-04 1.397723e-04
## [51] 1.444679e-04 1.452886e-04 1.501902e-04 1.513209e-04 1.564234e-04
## [56] 1.582807e-04 1.659658e-04 1.677662e-04 1.719678e-04 1.741575e-04
## [61] 1.803757e-04 1.910092e-04 1.933805e-04 1.973330e-04 2.171164e-04
## [66] 2.182968e-04 2.316741e-04 2.488440e-04 2.619285e-04 2.640971e-04
## [71] 2.793528e-04 2.793528e-04 2.982665e-04 3.143336e-04 3.237991e-04
## [76] 3.248600e-04 3.274774e-04 3.367856e-04 3.370570e-04 3.469428e-04
## [81] 3.598786e-04 3.673770e-04 3.707869e-04 3.784538e-04 3.791920e-04
## [86] 3.822240e-04 4.076553e-04 4.078931e-04 4.106850e-04 4.198135e-04
## [91] 4.279959e-04 4.317306e-04 4.579567e-04 4.597546e-04 4.605255e-04
## [96] 4.750752e-04 5.071705e-04 5.290726e-04 5.506797e-04 5.588360e-04
## [101] 6.350361e-04 6.447060e-04 6.503776e-04 6.643526e-04 6.921212e-04
## [106] 7.283228e-04 7.283228e-04 7.471458e-04 7.557416e-04 7.557416e-04
## [111] 7.610189e-04 7.828557e-04 8.020502e-04 8.152642e-04 8.179094e-04
## [116] 8.203292e-04 8.463181e-04 8.572285e-04 8.792227e-04 9.020160e-04
## [121] 9.124876e-04 9.140590e-04 9.284303e-04 9.566255e-04 9.575722e-04
## [126] 9.733166e-04 1.004175e-03 1.028137e-03 1.076199e-03 1.092147e-03
## [131] 1.098411e-03 1.122215e-03 1.157263e-03 1.167020e-03 1.210022e-03
## [136] 1.211037e-03 1.256567e-03 1.272799e-03 1.298750e-03 1.303613e-03
## [141] 1.320979e-03 1.339276e-03 1.357373e-03 1.358782e-03 1.358782e-03
## [146] 1.361844e-03 1.397868e-03 1.405549e-03 1.412108e-03 1.434202e-03
## [151] 1.483229e-03 1.538427e-03 1.546490e-03 1.602908e-03 1.602908e-03
## [156] 1.707637e-03 1.800493e-03 1.806511e-03 1.811276e-03 1.836921e-03
## [161] 1.944382e-03 1.972148e-03 2.013140e-03 2.084965e-03 2.094750e-03
## [166] 2.108920e-03 2.161401e-03 2.187565e-03 2.277706e-03 2.322425e-03
## [171] 2.366629e-03 2.379658e-03 2.416329e-03 2.518834e-03 2.575403e-03
## [176] 2.629347e-03 2.653624e-03 2.778003e-03 2.814702e-03 2.821963e-03
## [181] 2.916565e-03 2.926430e-03 3.068838e-03 3.097115e-03 3.229226e-03
## [186] 3.233614e-03 3.235368e-03 3.263003e-03 3.274285e-03 3.336970e-03
## [191] 3.366155e-03 3.424125e-03 3.496604e-03 3.506894e-03 3.611627e-03
## [196] 3.658319e-03 3.676212e-03 3.736416e-03 3.759101e-03 3.820079e-03
## [201] 3.867399e-03 3.984070e-03 4.056705e-03 4.116633e-03 4.151456e-03
## [206] 4.165554e-03 4.253232e-03 4.349885e-03 4.349885e-03 4.372056e-03
## [211] 4.401003e-03 4.460370e-03 4.462432e-03 4.546368e-03 4.546368e-03
## [216] 4.546754e-03 4.669400e-03 4.711984e-03 4.808173e-03 4.835880e-03
## [221] 4.876885e-03 5.094065e-03 5.129181e-03 5.143298e-03 5.211144e-03
## [226] 5.241116e-03 5.241116e-03 5.346863e-03 5.403152e-03 5.424907e-03
## [231] 5.605944e-03 5.685883e-03 5.726850e-03 5.772716e-03 6.065833e-03
## [236] 6.079005e-03 6.119886e-03 6.144539e-03 6.192004e-03 6.201571e-03
## [241] 6.257294e-03 6.270655e-03 6.416770e-03 6.720451e-03 6.799520e-03
## [246] 6.822677e-03 6.842026e-03 6.858929e-03 6.865760e-03 6.943901e-03
## [251] 7.113788e-03 7.233673e-03 7.402645e-03 7.487710e-03 7.508986e-03
## [256] 7.520972e-03 7.540246e-03 7.762205e-03 7.819068e-03 7.836691e-03
## [261] 7.901499e-03 7.976969e-03 8.245555e-03 8.485456e-03 8.538546e-03
## [266] 8.736633e-03 9.295120e-03 9.402667e-03 9.504856e-03 9.913375e-03
## [271] 9.932626e-03 1.002700e-02 1.002995e-02 1.017577e-02 1.021579e-02
## [276] 1.042973e-02 1.058320e-02 1.064633e-02 1.068373e-02 1.069139e-02
## [281] 1.076657e-02 1.077988e-02 1.147149e-02 1.181607e-02 1.198240e-02
## [286] 1.218875e-02 1.244285e-02 1.258221e-02 1.285875e-02 1.317904e-02
## [291] 1.371845e-02 1.374159e-02 1.435207e-02 1.468742e-02 1.583446e-02
## [296] 1.626130e-02 1.666577e-02 1.673607e-02 1.756830e-02 1.758942e-02
## [301] 1.843584e-02 1.872954e-02 1.934256e-02 1.981729e-02 2.014389e-02
## [306] 2.045307e-02 2.068281e-02 2.070380e-02 2.147755e-02 2.174184e-02
## [311] 2.182716e-02 2.183517e-02 2.209639e-02 2.213919e-02 2.268419e-02
## [316] 2.327770e-02 2.344854e-02 2.350527e-02 2.373014e-02 2.420980e-02
## [321] 2.455474e-02 2.460105e-02 2.496469e-02 2.700195e-02 2.829157e-02
## [326] 2.854826e-02 2.992250e-02 3.123315e-02 3.345343e-02 3.348643e-02
## [331] 3.462828e-02 3.512814e-02 3.646473e-02 3.705321e-02 3.875360e-02
## [336] 4.677001e-02 5.208223e-02 5.298463e-02## alpha area
## 1 0.006403124 0.000000e+00
## 2 0.011000000 1.239388e-07
## 3 0.026500000 1.777073e-06
## 4 0.027856777 1.989397e-06
## 5 0.028792360 2.163292e-06
## 6 0.030500000 2.606362e-06p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)4 Para la variable \(x_{2}\).
geom_indicesc <- indice1$results[[2]]$geom_indices
geom_indicescmenosr <- indice2$results[[2]]$geom_indices
geom_indicescmasr <- indice3$results[[2]]$geom_indices
geom_indicescmenosr2 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr2 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr2, geom_indicescmasr2)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))alpha.vals <- sort(unique(c(geom_indicescmenosr2$alpha, geom_indicescmasr2$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr2$alpha, geom_indicescmasr2$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr2$alpha, geom_indicescmenosr2$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.02018044 4.919256e-05
## [2,] 0.02147091 1.394103e-04
## [3,] 0.02470324 2.100808e-04
## [4,] 0.02540177 2.195322e-04
## [5,] 0.02692582 2.253926e-04
## [6,] 0.03041381 4.998547e-04
## [7,] 0.03376759 5.530796e-04
## [8,] 0.03579455 7.499706e-04
## [9,] 0.03946201 9.730748e-04
## [10,] 0.03992493 1.060742e-03
## [11,] 0.04200000 1.391576e-03
## [12,] 0.04294182 1.588818e-03
## [13,] 0.04382921 1.615168e-03
## [14,] 0.04810405 1.708986e-03
## [15,] 0.05001000 1.731744e-03
## [16,] 0.05020956 1.478886e-03
## [17,] 0.05093133 1.325416e-03
## [18,] 0.05380753 1.364250e-03
## [19,] 0.05749130 1.795422e-03
## [20,] 0.05996040 2.068730e-03
## [21,] 0.06067125 2.487251e-03
## [22,] 0.06250000 3.165127e-03
## [23,] 0.06280127 3.263559e-03
## [24,] 0.06280127 5.188203e-03
## [25,] 0.06469351 5.481444e-03
## [26,] 0.06469351 5.481444e-03
## [27,] 0.06470896 6.919279e-03
## [28,] 0.06719561 7.827879e-03
## [29,] 0.07011419 8.022038e-03
## [30,] 0.07097359 9.873732e-03
## [31,] 0.07102112 9.976035e-03
## [32,] 0.07180007 1.215710e-02
## [33,] 0.07294004 1.266270e-02
## [34,] 0.07426473 1.414962e-02
## [35,] 0.07432362 1.616300e-02
## [36,] 0.07544700 1.739761e-02
## [37,] 0.07566538 1.743813e-02
## [38,] 0.07615773 1.674220e-02
## [39,] 0.07788453 1.662443e-02
## [40,] 0.07826238 1.663864e-02
## [41,] 0.07864636 1.666709e-02
## [42,] 0.08062258 1.690682e-02
## [43,] 0.08062258 1.814581e-02
## [44,] 0.08068612 1.877362e-02
## [45,] 0.08095678 2.097067e-02
## [46,] 0.08137721 2.266459e-02
## [47,] 0.08139410 2.415320e-02
## [48,] 0.08139410 2.415320e-02
## [49,] 0.08231191 2.518693e-02
## [50,] 0.08271034 2.739085e-02
## [51,] 0.08276473 2.769444e-02
## [52,] 0.08341013 2.885954e-02
## [53,] 0.08403719 3.039848e-02
## [54,] 0.08403719 3.039848e-02
## [55,] 0.08509407 3.123306e-02
## [56,] 0.08575547 3.248788e-02
## [57,] 0.08597819 3.261806e-02
## [58,] 0.08608281 3.328947e-02
## [59,] 0.08640168 3.338397e-02
## [60,] 0.08703591 3.444838e-02
## [61,] 0.08914034 3.945706e-02
## [62,] 0.08995693 4.061082e-02
## [63,] 0.09024411 4.101159e-02
## [64,] 0.09055385 4.139006e-02
## [65,] 0.09058835 4.795386e-02
## [66,] 0.09073175 4.898471e-02
## [67,] 0.09106179 5.183673e-02
## [68,] 0.09150000 5.398139e-02
## [69,] 0.09178780 5.496530e-02
## [70,] 0.09212627 5.742675e-02
## [71,] 0.09222391 5.904757e-02
## [72,] 0.09222391 5.904757e-02
## [73,] 0.09222391 6.107897e-02
## [74,] 0.09250541 6.045016e-02
## [75,] 0.09257564 5.944555e-02
## [76,] 0.09388956 5.999833e-02
## [77,] 0.09396276 6.173392e-02
## [78,] 0.09406912 6.477898e-02
## [79,] 0.09501184 6.549232e-02
## [80,] 0.09502105 6.970401e-02
## [81,] 0.09512623 7.694608e-02
## [82,] 0.09529428 7.752185e-02
## [83,] 0.09552487 7.693440e-02
## [84,] 0.09552487 7.693440e-02
## [85,] 0.09602213 7.950099e-02
## [86,] 0.09604166 8.211761e-02
## [87,] 0.09610411 8.397357e-02
## [88,] 0.09688137 8.508498e-02
## [89,] 0.09688137 8.474484e-02
## [90,] 0.09740252 8.600927e-02
## [91,] 0.09947487 8.601274e-02
## [92,] 0.09963559 8.530374e-02
## [93,] 0.09964437 8.336546e-02
## [94,] 0.09972963 8.336838e-02
## [95,] 0.10003125 8.469580e-02
## [96,] 0.10040418 8.611032e-02
## [97,] 0.10099629 8.833390e-02
## [98,] 0.10162308 9.059248e-02
## [99,] 0.10376536 9.276340e-02
## [100,] 0.10404326 9.273975e-02
## [101,] 0.10490591 9.606294e-02
## [102,] 0.10491544 9.792412e-02
## [103,] 0.10550474 9.862591e-02
## [104,] 0.10597287 9.983893e-02
## [105,] 0.10680005 1.019116e-01
## [106,] 0.10705606 1.051056e-01
## [107,] 0.10707007 1.094392e-01
## [108,] 0.10717859 1.095037e-01
## [109,] 0.10748953 1.090238e-01
## [110,] 0.10770330 1.087560e-01
## [111,] 0.10925200 1.086987e-01
## [112,] 0.10965856 1.126944e-01
## [113,] 0.11007270 1.135705e-01
## [114,] 0.11032792 1.123080e-01
## [115,] 0.11059950 1.114310e-01
## [116,] 0.11114068 1.126297e-01
## [117,] 0.11115417 1.195108e-01
## [118,] 0.11115417 1.195108e-01
## [119,] 0.11115755 1.223201e-01
## [120,] 0.11144954 1.227990e-01
## [121,] 0.11171504 1.224438e-01
## [122,] 0.11285943 1.223696e-01
## [123,] 0.11289818 1.224085e-01
## [124,] 0.11294357 1.256227e-01
## [125,] 0.11352973 1.280682e-01
## [126,] 0.11352973 1.299463e-01
## [127,] 0.11362328 1.344886e-01
## [128,] 0.11450000 1.396632e-01
## [129,] 0.11461239 1.398864e-01
## [130,] 0.11503912 1.389452e-01
## [131,] 0.11505325 1.388692e-01
## [132,] 0.11536464 1.369707e-01
## [133,] 0.11600539 1.374506e-01
## [134,] 0.11706942 1.419089e-01
## [135,] 0.11718042 1.430348e-01
## [136,] 0.11737653 1.445742e-01
## [137,] 0.11766053 1.450505e-01
## [138,] 0.11830152 1.469967e-01
## [139,] 0.11884864 1.501798e-01
## [140,] 0.11884969 1.501841e-01
## [141,] 0.11950418 1.509076e-01
## [142,] 0.11954183 1.507008e-01
## [143,] 0.11954183 1.528149e-01
## [144,] 0.11992081 1.518710e-01
## [145,] 0.11992081 1.518710e-01
## [146,] 0.12014991 1.499386e-01
## [147,] 0.12062442 1.546599e-01
## [148,] 0.12091733 1.637870e-01
## [149,] 0.12110326 1.686469e-01
## [150,] 0.12116621 1.688479e-01
## [151,] 0.12159770 1.700020e-01
## [152,] 0.12320816 1.755256e-01
## [153,] 0.12582230 1.772603e-01
## [154,] 0.12617845 1.772334e-01
## [155,] 0.12683552 1.796901e-01
## [156,] 0.12709839 1.795788e-01
## [157,] 0.12731457 1.805167e-01
## [158,] 0.12863126 1.865692e-01
## [159,] 0.12884487 1.926452e-01
## [160,] 0.12887591 1.930692e-01
## [161,] 0.12955308 2.011726e-01
## [162,] 0.13001538 2.029986e-01
## [163,] 0.13086252 2.048001e-01
## [164,] 0.13148764 2.082297e-01
## [165,] 0.13449535 2.088702e-01
## [166,] 0.13487123 2.131522e-01
## [167,] 0.13520817 2.197060e-01
## [168,] 0.13686581 2.215034e-01
## [169,] 0.13845216 2.224939e-01
## [170,] 0.13926952 2.232911e-01
## [171,] 0.14010799 2.232295e-01
## [172,] 0.14020075 2.258723e-01
## [173,] 0.14058449 2.320001e-01
## [174,] 0.14074889 2.326391e-01
## [175,] 0.14188464 2.349743e-01
## [176,] 0.14244385 2.348190e-01
## [177,] 0.14302447 2.336573e-01
## [178,] 0.14317821 2.322750e-01
## [179,] 0.14350000 2.299976e-01
## [180,] 0.14534442 2.318852e-01
## [181,] 0.14536936 2.306065e-01
## [182,] 0.14547251 2.308320e-01
## [183,] 0.14560220 2.320255e-01
## [184,] 0.14630875 2.377558e-01
## [185,] 0.14760505 2.415665e-01
## [186,] 0.14767871 2.417721e-01
## [187,] 0.14869095 2.437890e-01
## [188,] 0.14869095 2.437890e-01
## [189,] 0.14894966 2.448573e-01
## [190,] 0.14920121 2.452614e-01
## [191,] 0.14938290 2.464485e-01
## [192,] 0.14949582 2.440425e-01
## [193,] 0.14985410 2.483663e-01
## [194,] 0.15138444 2.496590e-01
## [195,] 0.15182226 2.500014e-01
## [196,] 0.15277516 2.519946e-01
## [197,] 0.15289621 2.520702e-01
## [198,] 0.15344706 2.507843e-01
## [199,] 0.15367498 2.481009e-01
## [200,] 0.15435349 2.473548e-01
## [201,] 0.15502016 2.474313e-01
## [202,] 0.15598477 2.453247e-01
## [203,] 0.15598477 2.453247e-01
## [204,] 0.15601602 2.460062e-01
## [205,] 0.15609372 2.434505e-01
## [206,] 0.15616017 2.398296e-01
## [207,] 0.15741982 2.371856e-01
## [208,] 0.15879310 2.362606e-01
## [209,] 0.15959402 2.337385e-01
## [210,] 0.16058954 2.335908e-01
## [211,] 0.16070159 2.458281e-01
## [212,] 0.16082288 2.488522e-01
## [213,] 0.16095419 2.518737e-01
## [214,] 0.16155494 2.537051e-01
## [215,] 0.16233915 2.577380e-01
## [216,] 0.16363145 2.631303e-01
## [217,] 0.16368873 2.696814e-01
## [218,] 0.16394283 2.724671e-01
## [219,] 0.16426275 2.761380e-01
## [220,] 0.16573774 2.829839e-01
## [221,] 0.16580184 2.824567e-01
## [222,] 0.16604292 2.822955e-01
## [223,] 0.16648123 2.912974e-01
## [224,] 0.16648123 2.912974e-01
## [225,] 0.16680003 2.905927e-01
## [226,] 0.16714066 2.910083e-01
## [227,] 0.16770510 3.101936e-01
## [228,] 0.16905990 3.113911e-01
## [229,] 0.16918924 3.087431e-01
## [230,] 0.17023807 3.080962e-01
## [231,] 0.17110596 3.081846e-01
## [232,] 0.17133374 3.039878e-01
## [233,] 0.17154008 3.038384e-01
## [234,] 0.17270206 3.044840e-01
## [235,] 0.17278961 3.048619e-01
## [236,] 0.17300000 3.016985e-01
## [237,] 0.17372680 3.020123e-01
## [238,] 0.17397126 3.034359e-01
## [239,] 0.17439968 3.010583e-01
## [240,] 0.17507141 3.083450e-01
## [241,] 0.17534537 3.081362e-01
## [242,] 0.17560182 3.058329e-01
## [243,] 0.17570501 2.986868e-01
## [244,] 0.17613915 2.941528e-01
## [245,] 0.18027756 2.976820e-01
## [246,] 0.18140080 2.976922e-01
## [247,] 0.18337121 2.978874e-01
## [248,] 0.18501689 3.032793e-01
## [249,] 0.18577944 3.043794e-01
## [250,] 0.18988483 3.089282e-01
## [251,] 0.19006578 3.087606e-01
## [252,] 0.19006578 3.227233e-01
## [253,] 0.19012890 3.235793e-01
## [254,] 0.19248441 3.194467e-01
## [255,] 0.19262918 3.187050e-01
## [256,] 0.19420929 3.177654e-01
## [257,] 0.19450964 3.145903e-01
## [258,] 0.19641092 3.146421e-01
## [259,] 0.19724604 3.156191e-01
## [260,] 0.20238824 3.308225e-01
## [261,] 0.20300000 3.289667e-01
## [262,] 0.20376518 3.267585e-01
## [263,] 0.20504938 3.293686e-01
## [264,] 0.20535092 3.294390e-01
## [265,] 0.20706038 3.373548e-01
## [266,] 0.20885641 3.357059e-01
## [267,] 0.20892582 3.333070e-01
## [268,] 0.20898624 3.286790e-01
## [269,] 0.20967177 3.244824e-01
## [270,] 0.21120192 3.099635e-01
## [271,] 0.21128417 3.062090e-01
## [272,] 0.21239645 3.026674e-01
## [273,] 0.21425744 3.016912e-01
## [274,] 0.21543038 3.035848e-01
## [275,] 0.21739423 3.026389e-01
## [276,] 0.21777339 2.935779e-01
## [277,] 0.22754175 2.947128e-01
## [278,] 0.22808113 2.996534e-01
## [279,] 0.22886950 3.066391e-01
## [280,] 0.23005434 3.178645e-01
## [281,] 0.23325362 3.161881e-01
## [282,] 0.23505797 3.131822e-01
## [283,] 0.23992134 3.073737e-01
## [284,] 0.24000833 2.968684e-01
## [285,] 0.24748737 2.936062e-01
## [286,] 0.25519649 2.908013e-01
## [287,] 0.25640008 2.741962e-01
## [288,] 0.25870302 2.649559e-01
## [289,] 0.26054030 2.593866e-01
## [290,] 0.26160275 2.561339e-01
## [291,] 0.26288020 2.505048e-01
## [292,] 0.26454725 2.394784e-01
## [293,] 0.26622782 2.338800e-01
## [294,] 0.26864289 2.240522e-01
## [295,] 0.27280213 2.156415e-01
## [296,] 0.27436108 2.101475e-01
## [297,] 0.28925292 1.903975e-01
## [298,] 0.29054303 1.761821e-01
## [299,] 0.29610007 1.748734e-01
## [300,] 0.29610007 1.748734e-01
## [301,] 0.29618786 1.708443e-01
## [302,] 0.29763904 1.686579e-01
## [303,] 0.29769951 1.643059e-01
## [304,] 0.31329738 1.593809e-01
## [305,] 0.31715769 1.527778e-01
## [306,] 0.31715769 1.527778e-01
## [307,] 0.33568177 1.537926e-01
## [308,] 0.33864768 1.492265e-01
## [309,] 0.33915925 1.506474e-01
## [310,] 0.34033219 1.557826e-01
## [311,] 0.37955369 1.521600e-01
## [312,] 0.38527555 1.506996e-01
## [313,] 0.39300922 1.481949e-01
## [314,] 0.39395431 1.385102e-01
## [315,] 0.41270449 1.338462e-01
## [316,] 0.41831687 1.250355e-01
## [317,] 0.43229880 1.185509e-01
## [318,] 0.45262595 1.087905e-01
## [319,] 0.51032857 9.506492e-02
## [320,] 0.52236099 8.787769e-02
## [321,] 0.52259832 8.774719e-02
## [322,] 0.55148640 8.408755e-02
## [323,] 0.55381315 8.410634e-02
## [324,] 0.57747381 1.024165e-01
## [325,] 0.60609178 1.001165e-01
## [326,] 0.63496535 9.949764e-02
## [327,] 0.90067044 5.853768e-02
## [1] 0.000000e+00 1.799054e-07 8.589554e-07 1.012306e-06 1.355816e-06
## [6] 3.099304e-06 4.954208e-06 6.474372e-06 1.004308e-05 1.053412e-05
## [11] 1.342174e-05 1.491812e-05 1.635141e-05 2.365705e-05 2.695766e-05
## [16] 2.725279e-05 2.820943e-05 3.213329e-05 3.874722e-05 4.385512e-05
## [21] 4.562316e-05 5.141140e-05 5.239463e-05 5.239463e-05 6.276681e-05
## [26] 6.276681e-05 6.287375e-05 8.233891e-05 1.057519e-04 1.142373e-04
## [31] 1.147115e-04 1.241813e-04 1.386164e-04 1.573602e-04 1.583120e-04
## [36] 1.778562e-04 1.816644e-04 1.899074e-04 2.186144e-04 2.249013e-04
## [41] 2.313012e-04 2.647127e-04 2.647127e-04 2.659056e-04 2.715815e-04
## [46] 2.811104e-04 2.815185e-04 2.815185e-04 3.046351e-04 3.155485e-04
## [51] 3.170548e-04 3.356808e-04 3.547426e-04 3.547426e-04 3.877519e-04
## [56] 4.092394e-04 4.165044e-04 4.199870e-04 4.306321e-04 4.524804e-04
## [61] 5.355149e-04 5.686775e-04 5.804552e-04 5.932752e-04 5.949298e-04
## [66] 6.019539e-04 6.190623e-04 6.427174e-04 6.585363e-04 6.779737e-04
## [71] 6.837392e-04 6.837392e-04 6.837392e-04 7.007554e-04 7.049309e-04
## [76] 7.837638e-04 7.882824e-04 7.951726e-04 8.569134e-04 8.575553e-04
## [81] 8.656486e-04 8.786761e-04 8.964160e-04 8.964160e-04 9.359492e-04
## [86] 9.375526e-04 9.427969e-04 1.008930e-03 1.008930e-03 1.053753e-03
## [91] 1.232002e-03 1.245712e-03 1.246444e-03 1.253553e-03 1.279098e-03
## [96] 1.311212e-03 1.363514e-03 1.420297e-03 1.619022e-03 1.644795e-03
## [101] 1.727663e-03 1.728597e-03 1.786717e-03 1.833455e-03 1.917753e-03
## [106] 1.944662e-03 1.946195e-03 1.958078e-03 1.991979e-03 2.015227e-03
## [111] 2.183569e-03 2.229386e-03 2.276420e-03 2.305083e-03 2.335346e-03
## [116] 2.396298e-03 2.397911e-03 2.397911e-03 2.398324e-03 2.434180e-03
## [121] 2.466689e-03 2.606727e-03 2.611471e-03 2.617173e-03 2.692242e-03
## [126] 2.692242e-03 2.704823e-03 2.827268e-03 2.842990e-03 2.902283e-03
## [131] 2.904244e-03 2.946896e-03 3.034967e-03 3.185963e-03 3.201839e-03
## [136] 3.230192e-03 3.271386e-03 3.365610e-03 3.447776e-03 3.447934e-03
## [141] 3.546702e-03 3.552376e-03 3.552376e-03 3.609931e-03 3.609931e-03
## [146] 3.644281e-03 3.717669e-03 3.765644e-03 3.797001e-03 3.807630e-03
## [151] 3.880984e-03 4.163661e-03 4.627044e-03 4.690165e-03 4.808236e-03
## [156] 4.855441e-03 4.894465e-03 5.140118e-03 5.181270e-03 5.187263e-03
## [161] 5.323490e-03 5.417338e-03 5.590832e-03 5.721000e-03 6.349222e-03
## [166] 6.429342e-03 6.503369e-03 6.870541e-03 7.223494e-03 7.406004e-03
## [171] 7.593176e-03 7.614127e-03 7.703156e-03 7.741400e-03 8.008272e-03
## [176] 8.139585e-03 8.275252e-03 8.310962e-03 8.384973e-03 8.812666e-03
## [181] 8.818417e-03 8.842227e-03 8.872319e-03 9.040305e-03 9.353448e-03
## [186] 9.371256e-03 9.618031e-03 9.618031e-03 9.681376e-03 9.743072e-03
## [191] 9.787849e-03 9.815407e-03 9.904391e-03 1.028646e-02 1.039591e-02
## [196] 1.063604e-02 1.066655e-02 1.080469e-02 1.086124e-02 1.102907e-02
## [201] 1.119403e-02 1.143067e-02 1.143067e-02 1.143836e-02 1.145728e-02
## [206] 1.147321e-02 1.177198e-02 1.209644e-02 1.228364e-02 1.251618e-02
## [211] 1.254373e-02 1.257391e-02 1.260699e-02 1.275940e-02 1.296152e-02
## [216] 1.330156e-02 1.331701e-02 1.338624e-02 1.347459e-02 1.389199e-02
## [221] 1.391009e-02 1.397815e-02 1.410583e-02 1.410583e-02 1.419847e-02
## [226] 1.429759e-02 1.447268e-02 1.489455e-02 1.493449e-02 1.525762e-02
## [231] 1.552510e-02 1.559434e-02 1.565703e-02 1.601083e-02 1.603753e-02
## [236] 1.610100e-02 1.632050e-02 1.639468e-02 1.652366e-02 1.673079e-02
## [241] 1.681520e-02 1.689363e-02 1.692445e-02 1.705216e-02 1.828409e-02
## [246] 1.861847e-02 1.920543e-02 1.970453e-02 1.993663e-02 2.120490e-02
## [251] 2.126077e-02 2.126077e-02 2.128120e-02 2.203366e-02 2.207980e-02
## [256] 2.258190e-02 2.267639e-02 2.327461e-02 2.353819e-02 2.523935e-02
## [261] 2.544060e-02 2.569063e-02 2.611360e-02 2.621294e-02 2.678963e-02
## [266] 2.739257e-02 2.741571e-02 2.743557e-02 2.765801e-02 2.813230e-02
## [271] 2.815748e-02 2.849413e-02 2.905558e-02 2.941167e-02 3.000600e-02
## [276] 3.011732e-02 3.299618e-02 3.315780e-02 3.339955e-02 3.377617e-02
## [281] 3.478774e-02 3.535283e-02 3.684770e-02 3.687353e-02 3.906942e-02
## [286] 4.131124e-02 4.164126e-02 4.225144e-02 4.272801e-02 4.300014e-02
## [291] 4.332014e-02 4.371937e-02 4.411242e-02 4.465352e-02 4.555042e-02
## [296] 4.587803e-02 4.871340e-02 4.894070e-02 4.991248e-02 4.991248e-02
## [301] 4.992748e-02 5.017223e-02 5.018216e-02 5.266817e-02 5.325794e-02
## [306] 5.325794e-02 5.610680e-02 5.654939e-02 5.662646e-02 5.680918e-02
## [311] 6.277713e-02 6.363941e-02 6.478550e-02 6.491641e-02 6.742605e-02
## [316] 6.812779e-02 6.978536e-02 7.199676e-02 7.748226e-02 7.853964e-02
## [321] 7.856046e-02 8.098959e-02 8.118529e-02 8.360853e-02 8.647366e-02
## [326] 8.934651e-02 1.049003e-01## alpha area
## 1 0.02018044 0.000000e+00
## 2 0.02147091 1.799054e-07
## 3 0.02470324 8.589554e-07
## 4 0.02540177 1.012306e-06
## 5 0.02692582 1.355816e-06
## 6 0.03041381 3.099304e-06p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)5 Para la variable \(x_{3}\).
geom_indicesc <- indice1$results[[3]]$geom_indices
geom_indicescmenosr <- indice2$results[[3]]$geom_indices
geom_indicescmasr <- indice3$results[[3]]$geom_indices
geom_indicescmenosr3 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr3 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr3, geom_indicescmasr3)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))alpha.vals <- sort(unique(c(geom_indicescmenosr3$alpha, geom_indicescmasr3$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr3$alpha, geom_indicescmasr3$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr3$alpha, geom_indicescmenosr3$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.02385372 -1.137416e-05
## [2,] 0.03003748 9.290018e-05
## [3,] 0.03067572 1.073896e-04
## [4,] 0.03297347 3.250368e-05
## [5,] 0.04162031 2.319776e-06
## [6,] 0.04215744 2.058668e-04
## [7,] 0.04350000 5.651306e-04
## [8,] 0.04509989 7.734447e-04
## [9,] 0.04674666 9.189586e-04
## [10,] 0.04743416 9.468998e-04
## [11,] 0.04950000 9.512227e-04
## [12,] 0.04952020 9.556540e-04
## [13,] 0.05203124 1.656691e-03
## [14,] 0.05246189 1.749880e-03
## [15,] 0.05622277 1.909513e-03
## [16,] 0.05749130 1.599704e-03
## [17,] 0.05771698 2.163694e-03
## [18,] 0.05771698 2.163694e-03
## [19,] 0.05983519 2.451452e-03
## [20,] 0.05993538 2.461262e-03
## [21,] 0.06033448 2.601503e-03
## [22,] 0.06039247 2.284531e-03
## [23,] 0.06058259 2.250746e-03
## [24,] 0.06222741 2.714737e-03
## [25,] 0.06313478 2.802143e-03
## [26,] 0.06313478 2.802143e-03
## [27,] 0.06403124 3.514350e-03
## [28,] 0.06403124 4.167198e-03
## [29,] 0.06462198 4.632111e-03
## [30,] 0.06519394 4.597367e-03
## [31,] 0.06768309 5.057402e-03
## [32,] 0.06964194 5.351024e-03
## [33,] 0.07008745 6.223468e-03
## [34,] 0.07156116 6.751861e-03
## [35,] 0.07280110 6.702415e-03
## [36,] 0.07323933 6.726773e-03
## [37,] 0.07354590 7.757023e-03
## [38,] 0.07354590 7.757023e-03
## [39,] 0.07396114 8.749376e-03
## [40,] 0.07500000 9.650222e-03
## [41,] 0.07514819 1.075108e-02
## [42,] 0.08009994 1.274172e-02
## [43,] 0.08062258 1.518284e-02
## [44,] 0.08077747 1.576390e-02
## [45,] 0.08095678 1.681115e-02
## [46,] 0.08158431 1.873112e-02
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## [276] 4.328379e-02 4.456545e-02 4.480896e-02 4.577768e-02 4.579877e-02
## [281] 4.686940e-02 4.698820e-02 4.894246e-02 4.936891e-02 5.050060e-02
## [286] 5.082171e-02 5.148223e-02 5.569661e-02 5.590173e-02 5.809315e-02
## [291] 6.119099e-02 6.205995e-02 6.277262e-02 6.418048e-02 6.420686e-02
## [296] 6.770398e-02 6.842913e-02 6.932205e-02 6.957119e-02 7.029937e-02
## [301] 7.109787e-02 7.395648e-02 7.412956e-02 7.562097e-02 7.571677e-02
## [306] 7.583712e-02 7.668098e-02 7.964192e-02 8.012428e-02 8.204644e-02
## [311] 8.342278e-02 8.366194e-02 8.507267e-02 8.621628e-02 8.863278e-02
## [316] 8.869267e-02 9.035778e-02 9.639460e-02 9.676138e-02 9.823824e-02
## [321] 1.001660e-01 1.087096e-01 1.107757e-01 1.382919e-01 1.574354e-01
## [326] 1.595904e-01 1.738993e-01## alpha area
## 1 0.02385372 0.000000e+00
## 2 0.03003748 5.744720e-07
## 3 0.03067572 6.430131e-07
## 4 0.03297347 7.176984e-07
## 5 0.04162031 7.377571e-07
## 6 0.04215744 8.483355e-07p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)6 Ejemplo 2. Modelo de círculos concéntricos con agujeros.
n=100
cita <- round(runif(n, 0, 2*pi),2)
r1 <- round(runif(n, 3,4),2)
x1.center <- r1*cos(cita)
y1.center <- r1*sin(cita)
r2 <- round(runif(n, 6,7),2)
x2.center <- r2*cos(cita)
y2.center <- r2*sin(cita)
r3 <- round(runif(n, 10,11),2)
x3.center <- r3*cos(cita)
y3.center <- r3*sin(cita)
x1.ranks <- round(runif(n, 1, 2),2)
x2.ranks <- round(runif(n, 1, 2),2)
x3.ranks <- round(runif(n, 1, 2),2)
y1.ranks <- round(runif(n, 1, 2),2)
y2.ranks <- round(runif(n, 1, 2),2)
y3.ranks <- round(runif(n, 1, 2),2)
x1.lower <- x1.center - x1.ranks
x1.upper <- x1.center + x1.ranks
x2.lower <- x2.center - x2.ranks
x2.upper <- x2.center + x2.ranks
x3.lower <- x3.center - x3.ranks
x3.upper <- x3.center + x3.ranks
y1.lower <- y1.center - y1.ranks
y2.lower <- y2.center - y2.ranks
y3.lower <- y3.center - y3.ranks
y1.upper <- y1.center + y1.ranks
y2.upper <- y2.center + y2.ranks
y3.upper <- y3.center + y3.ranks
tabla <- data.frame(x1.lower,x1.upper,x2.lower,x2.upper,x3.lower,x3.upper,y1.lower,y1.upper,y2.lower,y2.upper,y3.lower,y3.upper, x1.center, x1.ranks,x2.center,x2.ranks,x3.center,x3.ranks, y1.center, y1.ranks, y2.center, y2.ranks, y3.center, y3.ranks)
# Primero fijamos un espacio adecuado para graficar todo
plot(NULL, xlim = c(-12, 12), ylim = c(-12, 12), xlab = "x", ylab = "y", asp = 1,
main = "Rectángulos simbólicos y sus centros")
# Dibujar los rectángulos del grupo 1
for (i in 1:n) {
rect(x1.lower[i], y1.lower[i], x1.upper[i], y1.upper[i], border = "blue", col = rgb(0, 0, 1, 0.2))
points(x1.center[i], y1.center[i], col = "blue", pch = 19, cex = 0.5)
}
# Rectángulos del grupo 2
for (i in 1:n) {
rect(x2.lower[i], y2.lower[i], x2.upper[i], y2.upper[i], border = "forestgreen", col = rgb(0, 0.6, 0, 0.2))
points(x2.center[i], y2.center[i], col = "forestgreen", pch = 19, cex = 0.5)
}
# Rectángulos del grupo 3
for (i in 1:n) {
rect(x3.lower[i], y3.lower[i], x3.upper[i], y3.upper[i], border = "darkorange", col = rgb(1, 0.5, 0, 0.2))
points(x3.center[i], y3.center[i], col = "darkorange", pch = 19, cex = 0.5)
}
legend("topright", legend = c("Grupo 1", "Grupo 2", "Grupo 3"),
col = c("blue", "forestgreen", "darkorange"), pch = 19, bty = "n")
Xc <- c(x1.center, x2.center, x3.center)
Yc <- c(y1.center, y2.center, y3.center)
Xl <- c(x1.lower, x2.lower, x3.lower)
Yl <- c(y1.lower, y2.lower, y3.lower)
Xu <- c(x1.upper, x2.upper, x3.upper)
Yu <- c(y1.upper, y2.upper, y3.upper)
indice1 <- spatgeom(y=Yc, x=Xc) ## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1
7 Para la variable \(x_{1}\).
geom_indicesc <- indice1$results[[1]]$geom_indices
geom_indicescmenosr <- indice2$results[[1]]$geom_indices
geom_indicescmasr <- indice3$results[[1]]$geom_indices
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr1, geom_indicescmasr1)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmenosr1$alpha, geom_indicescmasr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.05751881 -2.851600e-06
## [2,] 0.07104237 5.034950e-06
## [3,] 0.07929438 7.526247e-06
## [4,] 0.08378608 2.194501e-05
## [5,] 0.08510697 2.372027e-05
## [6,] 0.09448835 3.604006e-05
## [7,] 0.10077100 6.265201e-05
## [8,] 0.10448809 7.549548e-05
## [9,] 0.10510004 4.892473e-05
## [10,] 0.10649516 3.917267e-05
## [11,] 0.10805732 3.290353e-05
## [12,] 0.10856909 3.214808e-05
## [13,] 0.11249304 4.123253e-05
## [14,] 0.11453900 3.933572e-05
## [15,] 0.12265966 4.131728e-05
## [16,] 0.12447487 5.746840e-05
## [17,] 0.12515969 7.608835e-05
## [18,] 0.12601046 8.300276e-05
## [19,] 0.12654086 6.456527e-05
## [20,] 0.12673707 5.706473e-05
## [21,] 0.13117561 4.395024e-05
## [22,] 0.13122643 4.271595e-05
## [23,] 0.13138331 4.195758e-05
## [24,] 0.13196605 -1.467501e-06
## [25,] 0.13347483 3.093752e-05
## [26,] 0.13487940 6.590207e-05
## [27,] 0.13666559 7.664236e-05
## [28,] 0.13698212 2.814767e-05
## [29,] 0.14108375 2.784344e-05
## [30,] 0.14204654 2.241877e-05
## [31,] 0.14513139 6.710959e-06
## [32,] 0.14578325 4.390752e-06
## [33,] 0.14819941 -4.446061e-05
## [34,] 0.14967816 -4.700484e-05
## [35,] 0.15084774 -4.429050e-05
## [36,] 0.15111533 -1.507392e-05
## [37,] 0.15588017 -2.607831e-05
## [38,] 0.15810833 -2.318253e-05
## [39,] 0.15819744 -8.852952e-05
## [40,] 0.15857712 -9.523001e-05
## [41,] 0.16026817 -1.297848e-04
## [42,] 0.16369779 -1.412181e-04
## [43,] 0.16662958 -1.457363e-04
## [44,] 0.16700944 -1.449002e-04
## [45,] 0.16758356 -1.046129e-04
## [46,] 0.17358522 -1.055145e-04
## [47,] 0.17700929 -1.635855e-04
## [48,] 0.18032854 -1.671663e-04
## [49,] 0.18355639 -1.250827e-04
## [50,] 0.18692391 -6.579081e-05
## [51,] 0.19082829 -6.216795e-05
## [52,] 0.19407528 -8.923028e-05
## [53,] 0.19527559 -9.201903e-05
## [54,] 0.19850704 -9.297855e-05
## [55,] 0.20353335 -1.051307e-04
## [56,] 0.20474455 -7.256617e-05
## [57,] 0.20558321 -5.714380e-05
## [58,] 0.20698654 -1.273881e-04
## [59,] 0.20766314 -2.073486e-04
## [60,] 0.21022676 -1.763627e-04
## [61,] 0.21143459 -1.859849e-04
## [62,] 0.21220795 -2.205882e-04
## [63,] 0.21247185 -1.422611e-04
## [64,] 0.21257656 -1.395213e-04
## [65,] 0.21306687 -1.363023e-04
## [66,] 0.21322828 -1.447408e-04
## [67,] 0.21421787 -3.008333e-04
## [68,] 0.21959770 -2.693383e-04
## [69,] 0.21963777 -2.693068e-04
## [70,] 0.22160124 -2.623153e-04
## [71,] 0.22222029 -3.322516e-04
## [72,] 0.22315787 -3.279835e-04
## [73,] 0.22368154 -2.350356e-04
## [74,] 0.22451330 -9.401331e-05
## [75,] 0.22535793 -8.600012e-05
## [76,] 0.22736342 -6.571844e-05
## [77,] 0.22785171 -5.695945e-05
## [78,] 0.23035518 -7.106645e-05
## [79,] 0.23099590 3.630833e-05
## [80,] 0.23133272 6.773882e-05
## [81,] 0.23158479 1.081890e-04
## [82,] 0.23174957 9.848564e-05
## [83,] 0.23278386 9.616329e-05
## [84,] 0.23305077 8.199702e-05
## [85,] 0.23366207 5.447681e-05
## [86,] 0.23480390 4.144262e-05
## [87,] 0.23538897 3.759687e-05
## [88,] 0.23641187 1.378654e-05
## [89,] 0.23678760 -8.729911e-05
## [90,] 0.23685015 -1.502433e-04
## [91,] 0.23685968 -2.076334e-04
## [92,] 0.23943739 -1.976308e-04
## [93,] 0.24101272 -1.116319e-04
## [94,] 0.24108323 4.277189e-05
## [95,] 0.24224670 1.238565e-04
## [96,] 0.24238258 1.286826e-04
## [97,] 0.24440618 7.348935e-05
## [98,] 0.24534636 9.027253e-05
## [99,] 0.24543109 8.012560e-05
## [100,] 0.24602716 7.331216e-05
## [101,] 0.24824937 8.563602e-05
## [102,] 0.24860556 7.480575e-05
## [103,] 0.25051496 -9.233808e-05
## [104,] 0.25600747 -1.738584e-04
## [105,] 0.25698784 -1.837543e-04
## [106,] 0.25756298 -1.215985e-04
## [107,] 0.25996174 -7.723253e-05
## [108,] 0.26089015 -2.311284e-06
## [109,] 0.26102029 -5.464256e-05
## [110,] 0.26135688 -4.145180e-05
## [111,] 0.26197420 -6.021246e-05
## [112,] 0.26279392 -8.297598e-05
## [113,] 0.26424322 -7.271791e-05
## [114,] 0.26536118 -5.875311e-05
## [115,] 0.26614556 -1.055355e-04
## [116,] 0.26650648 -2.188283e-04
## [117,] 0.26858423 -2.524450e-04
## [118,] 0.26894438 -2.537658e-04
## [119,] 0.27075674 -2.279795e-04
## [120,] 0.27174739 -2.304471e-04
## [121,] 0.27283522 -2.855846e-04
## [122,] 0.27444322 -3.387329e-04
## [123,] 0.27507291 -1.563222e-04
## [124,] 0.27562571 -1.316054e-04
## [125,] 0.27617730 -1.958313e-05
## [126,] 0.27679246 3.873950e-05
## [127,] 0.27744283 8.526421e-05
## [128,] 0.27760892 4.939820e-05
## [129,] 0.27799266 6.289061e-05
## [130,] 0.27835671 2.968110e-05
## [131,] 0.28070853 -1.355062e-05
## [132,] 0.28123141 7.778902e-05
## [133,] 0.28138803 -5.709444e-06
## [134,] 0.28183948 1.521767e-05
## [135,] 0.28196095 3.555579e-06
## [136,] 0.28386319 -1.152022e-05
## [137,] 0.28446594 -5.219258e-05
## [138,] 0.28452431 -1.620840e-04
## [139,] 0.28730373 -2.201410e-04
## [140,] 0.28774953 -1.909496e-05
## [141,] 0.28778195 -4.930680e-06
## [142,] 0.28872323 5.075299e-05
## [143,] 0.28893446 6.304883e-05
## [144,] 0.28921269 8.450655e-06
## [145,] 0.28961345 -1.022775e-04
## [146,] 0.29093140 -1.503087e-04
## [147,] 0.29163035 1.694568e-05
## [148,] 0.29167288 1.565446e-05
## [149,] 0.29169469 -3.627734e-05
## [150,] 0.29215917 -8.890262e-05
## [151,] 0.29600330 -1.032189e-04
## [152,] 0.29674455 -1.423674e-04
## [153,] 0.29730140 -1.048808e-05
## [154,] 0.29744021 -8.302854e-06
## [155,] 0.29832650 -1.808607e-04
## [156,] 0.29952335 -1.762004e-04
## [157,] 0.29959715 -3.473698e-04
## [158,] 0.29987943 -3.428061e-04
## [159,] 0.30105946 -2.480391e-04
## [160,] 0.30280613 -2.714086e-04
## [161,] 0.30304863 -2.859202e-04
## [162,] 0.30603081 -3.068400e-04
## [163,] 0.30643001 -4.418881e-04
## [164,] 0.30932704 -4.259526e-04
## [165,] 0.31011770 -5.612857e-04
## [166,] 0.31036459 -5.784469e-04
## [167,] 0.31079487 -5.892572e-04
## [168,] 0.31179108 -5.905017e-04
## [169,] 0.31360124 -5.492938e-04
## [170,] 0.31412360 -5.631944e-04
## [171,] 0.31429273 -4.355432e-04
## [172,] 0.31444431 -3.066231e-04
## [173,] 0.31728258 -3.107952e-04
## [174,] 0.31732319 -4.653934e-04
## [175,] 0.31783631 -5.236058e-04
## [176,] 0.31871113 -5.781340e-04
## [177,] 0.31953305 -5.377470e-04
## [178,] 0.32231124 -4.788717e-04
## [179,] 0.32472166 -3.693348e-04
## [180,] 0.32584379 -3.303317e-04
## [181,] 0.32709657 -2.982085e-04
## [182,] 0.32715059 -2.969039e-04
## [183,] 0.32950585 -1.580952e-04
## [184,] 0.33020291 -1.086771e-04
## [185,] 0.33042521 2.149014e-04
## [186,] 0.33447663 4.210124e-04
## [187,] 0.33628097 5.357294e-04
## [188,] 0.33738744 4.470406e-04
## [189,] 0.33791436 7.192453e-04
## [190,] 0.33803452 7.395766e-04
## [191,] 0.33865688 8.921169e-04
## [192,] 0.33876732 1.125277e-03
## [193,] 0.33956078 1.180033e-03
## [194,] 0.34039404 1.199646e-03
## [195,] 0.34111002 8.053825e-04
## [196,] 0.34203455 5.661808e-04
## [197,] 0.34215683 5.661112e-04
## [198,] 0.34229746 1.168168e-03
## [199,] 0.34419304 1.249671e-03
## [200,] 0.34427179 1.241853e-03
## [201,] 0.34500948 1.197256e-03
## [202,] 0.34502553 1.199516e-03
## [203,] 0.34714929 1.218719e-03
## [204,] 0.35004225 1.189331e-03
## [205,] 0.35086535 1.029870e-03
## [206,] 0.35124282 1.162275e-03
## [207,] 0.35160318 1.296987e-03
## [208,] 0.35184809 1.354345e-03
## [209,] 0.35188283 1.095812e-03
## [210,] 0.35198978 8.856017e-04
## [211,] 0.35203455 9.050098e-04
## [212,] 0.35342684 1.052643e-03
## [213,] 0.35445163 1.080263e-03
## [214,] 0.35643644 1.139542e-03
## [215,] 0.35675019 1.086970e-03
## [216,] 0.35720956 1.014751e-03
## [217,] 0.35765094 8.540180e-04
## [218,] 0.35957042 1.034596e-03
## [219,] 0.36012807 1.081820e-03
## [220,] 0.36094842 1.219538e-03
## [221,] 0.36199345 1.302021e-03
## [222,] 0.36263783 1.450874e-03
## [223,] 0.36298584 1.462196e-03
## [224,] 0.36312219 1.462885e-03
## [225,] 0.36339844 1.319648e-03
## [226,] 0.36446361 1.573100e-03
## [227,] 0.36513121 1.613607e-03
## [228,] 0.36715135 1.653967e-03
## [229,] 0.36800835 1.688514e-03
## [230,] 0.36834180 1.279192e-03
## [231,] 0.36986425 1.021136e-03
## [232,] 0.36987364 9.432672e-04
## [233,] 0.36999967 9.150602e-04
## [234,] 0.37021891 9.061404e-04
## [235,] 0.37045702 1.163316e-03
## [236,] 0.37056665 1.292688e-03
## [237,] 0.37153721 1.244116e-03
## [238,] 0.37196381 1.216705e-03
## [239,] 0.37238601 1.133693e-03
## [240,] 0.37317619 8.427267e-04
## [241,] 0.37367706 7.150981e-04
## [242,] 0.37543026 7.455629e-04
## [243,] 0.37553338 1.833570e-04
## [244,] 0.37582009 1.884502e-04
## [245,] 0.37698666 2.571199e-04
## [246,] 0.37802288 3.490125e-04
## [247,] 0.37879585 4.255290e-04
## [248,] 0.37997065 8.285717e-04
## [249,] 0.38040903 1.155404e-03
## [250,] 0.38065633 1.372576e-03
## [251,] 0.38111665 1.637583e-03
## [252,] 0.38291659 1.679891e-03
## [253,] 0.38375659 1.947927e-03
## [254,] 0.38623637 1.929568e-03
## [255,] 0.38632173 1.677844e-03
## [256,] 0.38642587 1.093238e-03
## [257,] 0.38851314 1.091705e-03
## [258,] 0.38893645 1.363665e-03
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## [1055,] 3.29452704 1.965198e-03
## [1] 0.000000e+00 6.809045e-08 1.301971e-07 2.287676e-07 2.600994e-07
## [6] 5.982050e-07 9.918256e-07 1.272449e-06 1.302389e-06 1.357039e-06
## [11] 1.408440e-06 1.424892e-06 1.586687e-06 1.667166e-06 2.002689e-06
## [16] 2.107006e-06 2.159113e-06 2.229729e-06 2.263975e-06 2.275172e-06
## [21] 2.470246e-06 2.472418e-06 2.479000e-06 2.478144e-06 2.524822e-06
## [26] 2.617387e-06 2.754284e-06 2.763194e-06 2.877397e-06 2.898982e-06
## [31] 2.919684e-06 2.922546e-06 2.815123e-06 2.745614e-06 2.693813e-06
## [36] 2.689779e-06 2.565520e-06 2.513866e-06 2.505977e-06 2.469821e-06
## [41] 2.250348e-06 1.766024e-06 1.338754e-06 1.283713e-06 1.223653e-06
## [46] 5.903911e-07 3.026314e-08 -5.246049e-07 -9.283528e-07 -1.149905e-06
## [51] -1.392632e-06 -1.682361e-06 -1.792813e-06 -2.093269e-06 -2.621688e-06
## [56] -2.709580e-06 -2.757505e-06 -2.936272e-06 -3.076562e-06 -3.528689e-06
## [61] -3.753329e-06 -3.923921e-06 -3.961465e-06 -3.976074e-06 -4.042904e-06
## [66] -4.066267e-06 -4.363968e-06 -5.812963e-06 -5.823753e-06 -6.338801e-06
## [71] -6.544482e-06 -6.851994e-06 -6.975074e-06 -7.053271e-06 -7.125909e-06
## [76] -7.257707e-06 -7.285519e-06 -7.463432e-06 -7.440168e-06 -7.417353e-06
## [81] -7.390081e-06 -7.373853e-06 -7.274392e-06 -7.252506e-06 -7.219204e-06
## [86] -7.171884e-06 -7.149887e-06 -7.135785e-06 -7.168586e-06 -7.177984e-06
## [91] -7.179963e-06 -7.689397e-06 -7.865254e-06 -7.862238e-06 -7.718134e-06
## [96] -7.700649e-06 -7.551935e-06 -7.467064e-06 -7.460274e-06 -7.416575e-06
## [101] -7.226274e-06 -7.199629e-06 -7.375939e-06 -8.330858e-06 -8.511006e-06
## [106] -8.580942e-06 -8.766204e-06 -8.768350e-06 -8.775461e-06 -8.789413e-06
## [111] -8.826584e-06 -8.894601e-06 -8.999991e-06 -9.065675e-06 -9.148454e-06
## [116] -9.227434e-06 -9.751951e-06 -9.843344e-06 -1.025653e-05 -1.048482e-05
## [121] -1.079549e-05 -1.134017e-05 -1.143860e-05 -1.151135e-05 -1.152216e-05
## [126] -1.149833e-05 -1.144287e-05 -1.143467e-05 -1.141053e-05 -1.139973e-05
## [131] -1.143160e-05 -1.139092e-05 -1.139182e-05 -1.138495e-05 -1.138452e-05
## [136] -1.140643e-05 -1.143789e-05 -1.144735e-05 -1.205921e-05 -1.206773e-05
## [141] -1.206789e-05 -1.202011e-05 -1.200679e-05 -1.200444e-05 -1.204543e-05
## [146] -1.224353e-05 -1.223169e-05 -1.223102e-05 -1.223181e-05 -1.227311e-05
## [151] -1.266989e-05 -1.277542e-05 -1.278126e-05 -1.278242e-05 -1.294271e-05
## [156] -1.315360e-05 -1.317923e-05 -1.327600e-05 -1.356870e-05 -1.404275e-05
## [161] -1.411209e-05 -1.502714e-05 -1.520354e-05 -1.643754e-05 -1.688133e-05
## [166] -1.702414e-05 -1.727769e-05 -1.786595e-05 -1.886026e-05 -1.915445e-05
## [171] -1.922812e-05 -1.927459e-05 -2.015672e-05 -2.017562e-05 -2.044429e-05
## [176] -2.095005e-05 -2.139203e-05 -2.272243e-05 -2.361268e-05 -2.398336e-05
## [181] -2.435695e-05 -2.437299e-05 -2.474534e-05 -2.482110e-05 -2.477332e-05
## [186] -2.306763e-05 -2.210099e-05 -2.160635e-05 -2.122737e-05 -2.113849e-05
## [191] -2.058328e-05 -2.045900e-05 -1.952270e-05 -1.852308e-05 -1.794644e-05
## [196] -1.742299e-05 -1.735377e-05 -1.718949e-05 -1.482064e-05 -1.472284e-05
## [201] -1.383964e-05 -1.382039e-05 -1.123212e-05 -7.791435e-06 -6.943742e-06
## [206] -6.505023e-06 -6.037644e-06 -5.705948e-06 -5.667878e-06 -5.573163e-06
## [211] -5.532645e-06 -4.067066e-06 -2.960017e-06 -6.982460e-07 -3.572138e-07
## [216] 1.089355e-07 4.858791e-07 2.471773e-06 3.075043e-06 4.075492e-06
## [221] 5.436140e-06 6.371062e-06 6.879927e-06 7.079380e-06 7.443940e-06
## [226] 9.119561e-06 1.019679e-05 1.353804e-05 1.498511e-05 1.541165e-05
## [231] 1.696627e-05 1.697513e-05 1.709045e-05 1.728912e-05 1.756612e-05
## [236] 1.770784e-05 1.891533e-05 1.943438e-05 1.991302e-05 2.057892e-05
## [241] 2.093709e-05 2.224421e-05 2.226312e-05 2.231715e-05 2.261710e-05
## [246] 2.297875e-05 2.330768e-05 2.428108e-05 2.478759e-05 2.512703e-05
## [251] 2.588084e-05 2.890455e-05 3.054081e-05 3.532570e-05 3.546893e-05
## [256] 3.558277e-05 3.786146e-05 3.843872e-05 4.047647e-05 4.054040e-05
## [261] 4.202734e-05 4.400054e-05 4.550778e-05 4.804107e-05 4.902950e-05
## [266] 4.987498e-05 5.026324e-05 5.123372e-05 5.214436e-05 5.545937e-05
## [271] 5.782239e-05 5.926571e-05 5.960836e-05 6.029896e-05 6.222956e-05
## [276] 6.446070e-05 6.534807e-05 6.838480e-05 6.990953e-05 7.449212e-05
## [281] 7.541766e-05 7.594103e-05 7.626878e-05 7.898000e-05 7.994969e-05
## [286] 8.098387e-05 8.214611e-05 8.278977e-05 8.576777e-05 8.608111e-05
## [291] 8.710977e-05 8.879300e-05 8.935788e-05 8.999550e-05 9.087812e-05
## [296] 9.091635e-05 9.186903e-05 9.293038e-05 9.459586e-05 9.519560e-05
## [301] 9.561285e-05 9.665263e-05 9.731989e-05 9.753693e-05 9.761117e-05
## [306] 9.763400e-05 9.810879e-05 9.839107e-05 9.830445e-05 9.824888e-05
## [311] 9.792146e-05 9.791910e-05 9.799657e-05 9.823080e-05 9.858684e-05
## [316] 9.861280e-05 9.856230e-05 9.856223e-05 9.886718e-05 9.914254e-05
## [321] 9.968131e-05 1.058725e-04 1.059156e-04 1.063259e-04 1.065169e-04
## [326] 1.080578e-04 1.087676e-04 1.102718e-04 1.106456e-04 1.106427e-04
## [331] 1.102400e-04 1.101309e-04 1.092555e-04 1.090513e-04 1.091729e-04
## [336] 1.092359e-04 1.096770e-04 1.117899e-04 1.120652e-04 1.130392e-04
## [341] 1.131890e-04 1.132353e-04 1.136337e-04 1.136421e-04 1.139020e-04
## [346] 1.141350e-04 1.143405e-04 1.144224e-04 1.145714e-04 1.148663e-04
## [351] 1.148731e-04 1.166449e-04 1.177958e-04 1.178424e-04 1.179302e-04
## [356] 1.177204e-04 1.152458e-04 1.150784e-04 1.149325e-04 1.162807e-04
## [361] 1.166876e-04 1.171490e-04 1.173320e-04 1.185569e-04 1.189368e-04
## [366] 1.191614e-04 1.196162e-04 1.198493e-04 1.211378e-04 1.226964e-04
## [371] 1.231880e-04 1.257019e-04 1.270796e-04 1.282798e-04 1.292788e-04
## [376] 1.308748e-04 1.312722e-04 1.313501e-04 1.314133e-04 1.320430e-04
## [381] 1.331504e-04 1.331366e-04 1.331361e-04 1.335188e-04 1.336809e-04
## [386] 1.342599e-04 1.352332e-04 1.369290e-04 1.386468e-04 1.395805e-04
## [391] 1.477973e-04 1.487416e-04 1.494150e-04 1.512666e-04 1.552129e-04
## [396] 1.560792e-04 1.576169e-04 1.579600e-04 1.655445e-04 1.668729e-04
## [401] 1.690147e-04 1.694854e-04 1.758422e-04 1.759626e-04 1.761664e-04
## [406] 1.762209e-04 1.817849e-04 1.821804e-04 1.834617e-04 1.835447e-04
## [411] 1.873495e-04 1.886194e-04 1.892349e-04 1.896550e-04 1.931725e-04
## [416] 1.939934e-04 1.940303e-04 1.956609e-04 2.011475e-04 2.013909e-04
## [421] 2.019317e-04 2.019963e-04 2.026392e-04 2.050080e-04 2.062047e-04
## [426] 2.062345e-04 2.064048e-04 2.071690e-04 2.076694e-04 2.105554e-04
## [431] 2.107305e-04 2.109283e-04 2.110599e-04 2.110803e-04 2.118126e-04
## [436] 2.118788e-04 2.118402e-04 2.116245e-04 2.113425e-04 2.109237e-04
## [441] 2.105221e-04 2.100023e-04 2.099949e-04 2.100855e-04 2.102054e-04
## [446] 2.105417e-04 2.132661e-04 2.133428e-04 2.140349e-04 2.157590e-04
## [451] 2.162783e-04 2.180051e-04 2.228170e-04 2.233767e-04 2.421107e-04
## [456] 2.633480e-04 2.642377e-04 2.648224e-04 2.650905e-04 2.669145e-04
## [461] 2.714147e-04 2.734109e-04 2.788596e-04 2.791378e-04 2.934075e-04
## [466] 2.973297e-04 2.993303e-04 3.003745e-04 3.119597e-04 3.142360e-04
## [471] 3.194512e-04 3.208895e-04 3.250214e-04 3.366078e-04 3.417719e-04
## [476] 3.433709e-04 3.576124e-04 3.707027e-04 3.709277e-04 3.784172e-04
## [481] 3.852026e-04 3.890778e-04 4.018917e-04 4.216441e-04 4.252740e-04
## [486] 4.355172e-04 4.374389e-04 4.393077e-04 4.470391e-04 4.559091e-04
## [491] 4.560504e-04 4.570873e-04 4.657963e-04 5.035892e-04 5.055701e-04
## [496] 5.335635e-04 5.388536e-04 5.430530e-04 5.439253e-04 5.450306e-04
## [501] 5.463708e-04 5.478408e-04 5.666969e-04 5.954090e-04 6.097974e-04
## [506] 6.532561e-04 6.614450e-04 6.684607e-04 6.822337e-04 6.852159e-04
## [511] 7.036571e-04 7.434847e-04 7.636160e-04 7.821754e-04 7.996555e-04
## [516] 8.054063e-04 8.183081e-04 8.475189e-04 8.626425e-04 8.706705e-04
## [521] 8.840705e-04 8.973795e-04 9.253893e-04 9.645838e-04 9.718968e-04
## [526] 9.738290e-04 9.768567e-04 1.062926e-03 1.069557e-03 1.108398e-03
## [531] 1.130833e-03 1.175752e-03 1.215396e-03 1.217996e-03 1.242111e-03
## [536] 1.245919e-03 1.250335e-03 1.267187e-03 1.300743e-03 1.315506e-03
## [541] 1.329474e-03 1.399315e-03 1.420250e-03 1.420811e-03 1.477026e-03
## [546] 1.499759e-03 1.526808e-03 1.542092e-03 1.553369e-03 1.568851e-03
## [551] 1.581712e-03 1.596877e-03 1.675478e-03 1.723990e-03 1.727113e-03
## [556] 1.728765e-03 1.736433e-03 1.783410e-03 1.807152e-03 1.858979e-03
## [561] 1.914561e-03 1.922297e-03 1.954825e-03 1.980871e-03 2.005731e-03
## [566] 2.084938e-03 2.086535e-03 2.096796e-03 2.097248e-03 2.101801e-03
## [571] 2.104649e-03 2.116918e-03 2.123260e-03 2.178421e-03 2.239831e-03
## [576] 2.250598e-03 2.312568e-03 2.317146e-03 2.364946e-03 2.365683e-03
## [581] 2.388791e-03 2.441207e-03 2.471706e-03 2.517740e-03 2.539683e-03
## [586] 2.547753e-03 2.566312e-03 2.572506e-03 2.629522e-03 2.636561e-03
## [591] 2.650496e-03 2.666649e-03 2.706262e-03 2.731076e-03 2.749665e-03
## [596] 2.752340e-03 2.766718e-03 2.778842e-03 2.780702e-03 2.812093e-03
## [601] 2.814577e-03 2.814625e-03 2.825248e-03 2.865194e-03 2.866515e-03
## [606] 2.877263e-03 2.881732e-03 2.895788e-03 2.915903e-03 2.958498e-03
## [611] 2.987793e-03 2.997928e-03 3.053530e-03 3.101583e-03 3.148248e-03
## [616] 3.187946e-03 3.189973e-03 3.198852e-03 3.225887e-03 3.250524e-03
## [621] 3.253564e-03 3.269490e-03 3.293825e-03 3.343262e-03 3.347859e-03
## [626] 3.374908e-03 3.375517e-03 3.380525e-03 3.382803e-03 3.392380e-03
## [631] 3.438048e-03 3.467534e-03 3.533629e-03 3.586910e-03 3.666938e-03
## [636] 3.683972e-03 3.708280e-03 3.729865e-03 3.737228e-03 3.773088e-03
## [641] 3.793158e-03 3.843826e-03 3.932251e-03 3.969387e-03 3.971166e-03
## [646] 4.002670e-03 4.002993e-03 4.014222e-03 4.092484e-03 4.101273e-03
## [651] 4.116240e-03 4.172668e-03 4.209258e-03 4.226489e-03 4.253428e-03
## [656] 4.268379e-03 4.290877e-03 4.328359e-03 4.369465e-03 4.417616e-03
## [661] 4.418101e-03 4.472895e-03 4.534289e-03 4.561821e-03 4.567148e-03
## [666] 4.575872e-03 4.607558e-03 4.669803e-03 4.686069e-03 4.732613e-03
## [671] 4.782944e-03 4.786248e-03 4.805189e-03 4.827649e-03 4.884553e-03
## [676] 4.924106e-03 4.963695e-03 5.007642e-03 5.046211e-03 5.127521e-03
## [681] 5.129163e-03 5.213558e-03 5.287425e-03 5.382621e-03 5.403901e-03
## [686] 5.439120e-03 5.493896e-03 5.544642e-03 5.611753e-03 5.636168e-03
## [691] 5.661325e-03 5.758837e-03 5.782625e-03 5.865388e-03 5.985479e-03
## [696] 6.289235e-03 6.358179e-03 6.524165e-03 6.549468e-03 6.639991e-03
## [701] 6.679289e-03 6.916434e-03 7.060604e-03 7.181597e-03 7.186236e-03
## [706] 7.208354e-03 7.265974e-03 7.268533e-03 7.284917e-03 7.335641e-03
## [711] 7.421184e-03 7.430256e-03 7.469675e-03 7.531363e-03 7.540944e-03
## [716] 7.546501e-03 7.690677e-03 7.724547e-03 7.753447e-03 7.824828e-03
## [721] 7.881495e-03 7.882661e-03 7.961000e-03 7.983838e-03 8.093154e-03
## [726] 8.157447e-03 8.213895e-03 8.252704e-03 8.292952e-03 8.333929e-03
## [731] 8.343924e-03 8.360250e-03 8.373534e-03 8.421985e-03 8.435201e-03
## [736] 8.486459e-03 8.552245e-03 8.681108e-03 8.740994e-03 8.892466e-03
## [741] 8.922972e-03 9.095996e-03 9.178070e-03 9.346918e-03 9.349610e-03
## [746] 9.396858e-03 9.503894e-03 9.673569e-03 9.685474e-03 9.830782e-03
## [751] 9.856289e-03 9.951465e-03 9.970463e-03 9.970860e-03 1.007264e-02
## [756] 1.008671e-02 1.014048e-02 1.021155e-02 1.023521e-02 1.027798e-02
## [761] 1.029112e-02 1.049771e-02 1.051612e-02 1.055656e-02 1.056006e-02
## [766] 1.061518e-02 1.065869e-02 1.097816e-02 1.104801e-02 1.116791e-02
## [771] 1.139182e-02 1.144948e-02 1.149939e-02 1.169985e-02 1.173767e-02
## [776] 1.174145e-02 1.176873e-02 1.184005e-02 1.201210e-02 1.223037e-02
## [781] 1.224302e-02 1.227948e-02 1.235717e-02 1.240009e-02 1.253505e-02
## [786] 1.272076e-02 1.284645e-02 1.289429e-02 1.297650e-02 1.301828e-02
## [791] 1.306116e-02 1.336508e-02 1.337682e-02 1.357121e-02 1.359128e-02
## [796] 1.363169e-02 1.366681e-02 1.374847e-02 1.378229e-02 1.378686e-02
## [801] 1.401012e-02 1.408550e-02 1.415275e-02 1.426955e-02 1.435813e-02
## [806] 1.447339e-02 1.451451e-02 1.474491e-02 1.479782e-02 1.482380e-02
## [811] 1.496929e-02 1.537067e-02 1.557316e-02 1.579716e-02 1.583446e-02
## [816] 1.584400e-02 1.596827e-02 1.611560e-02 1.635842e-02 1.638366e-02
## [821] 1.641301e-02 1.643339e-02 1.644307e-02 1.644673e-02 1.658709e-02
## [826] 1.665921e-02 1.669630e-02 1.673115e-02 1.705415e-02 1.711655e-02
## [831] 1.722993e-02 1.723904e-02 1.724475e-02 1.751993e-02 1.763938e-02
## [836] 1.787035e-02 1.791136e-02 1.798655e-02 1.806449e-02 1.806682e-02
## [841] 1.813037e-02 1.825226e-02 1.826115e-02 1.829917e-02 1.834331e-02
## [846] 1.836402e-02 1.908761e-02 1.950887e-02 1.951579e-02 1.959331e-02
## [851] 1.972767e-02 1.981416e-02 1.989974e-02 2.000906e-02 2.021012e-02
## [856] 2.022982e-02 2.031226e-02 2.031929e-02 2.041615e-02 2.043963e-02
## [861] 2.044132e-02 2.064088e-02 2.068073e-02 2.073184e-02 2.073736e-02
## [866] 2.075222e-02 2.075428e-02 2.076226e-02 2.076868e-02 2.077378e-02
## [871] 2.079473e-02 2.081805e-02 2.081890e-02 2.081890e-02 2.081694e-02
## [876] 2.081621e-02 2.080481e-02 2.077021e-02 2.076230e-02 2.068235e-02
## [881] 2.066632e-02 2.066537e-02 2.061275e-02 2.057211e-02 2.049870e-02
## [886] 2.048782e-02 2.048138e-02 2.048174e-02 2.052214e-02 2.052920e-02
## [891] 2.058663e-02 2.058791e-02 2.060567e-02 2.064128e-02 2.065527e-02
## [896] 2.066350e-02 2.066488e-02 2.067937e-02 2.075183e-02 2.093869e-02
## [901] 2.115785e-02 2.119299e-02 2.120943e-02 2.135458e-02 2.137169e-02
## [906] 2.140017e-02 2.162020e-02 2.168968e-02 2.191825e-02 2.206210e-02
## [911] 2.215940e-02 2.227834e-02 2.228073e-02 2.228275e-02 2.229640e-02
## [916] 2.229658e-02 2.242077e-02 2.261707e-02 2.281376e-02 2.328486e-02
## [921] 2.337092e-02 2.346952e-02 2.359580e-02 2.367549e-02 2.429661e-02
## [926] 2.433143e-02 2.454004e-02 2.454517e-02 2.455391e-02 2.455506e-02
## [931] 2.463800e-02 2.465726e-02 2.468520e-02 2.473417e-02 2.481264e-02
## [936] 2.498690e-02 2.506513e-02 2.525910e-02 2.536193e-02 2.538771e-02
## [941] 2.561795e-02 2.564728e-02 2.570233e-02 2.573929e-02 2.576950e-02
## [946] 2.581249e-02 2.587874e-02 2.591765e-02 2.603081e-02 2.605475e-02
## [951] 2.607566e-02 2.615127e-02 2.621285e-02 2.624594e-02 2.628101e-02
## [956] 2.630245e-02 2.632555e-02 2.635929e-02 2.636812e-02 2.639961e-02
## [961] 2.653286e-02 2.654157e-02 2.655998e-02 2.658220e-02 2.659850e-02
## [966] 2.690553e-02 2.695782e-02 2.734616e-02 2.736412e-02 2.752511e-02
## [971] 2.754877e-02 2.764383e-02 2.781355e-02 2.783304e-02 2.790200e-02
## [976] 2.805784e-02 2.820658e-02 2.829758e-02 2.840073e-02 2.846629e-02
## [981] 2.850817e-02 2.850939e-02 2.848070e-02 2.847525e-02 2.842021e-02
## [986] 2.840947e-02 2.839386e-02 2.839291e-02 2.837215e-02 2.836668e-02
## [991] 2.837284e-02 2.840079e-02 2.859615e-02 2.871852e-02 2.879672e-02
## [996] 2.882966e-02 2.885850e-02 2.913418e-02 2.917566e-02 2.928167e-02
## [1001] 2.931551e-02 2.934791e-02 2.937936e-02 2.944128e-02 2.945098e-02
## [1006] 2.947739e-02 2.971470e-02 2.983991e-02 2.986524e-02 2.987428e-02
## [1011] 2.987940e-02 2.998062e-02 2.998090e-02 2.997943e-02 2.997007e-02
## [1016] 2.995955e-02 2.962840e-02 2.961640e-02 2.956628e-02 2.956164e-02
## [1021] 2.963830e-02 2.963840e-02 2.983540e-02 3.004340e-02 3.012862e-02
## [1026] 3.022265e-02 3.028023e-02 3.028237e-02 3.034565e-02 3.238518e-02
## [1031] 3.242400e-02 3.254227e-02 3.293515e-02 3.300160e-02 3.342062e-02
## [1036] 3.370134e-02 3.372424e-02 3.410860e-02 3.432752e-02 3.494187e-02
## [1041] 3.531027e-02 3.553685e-02 3.566269e-02 3.670992e-02 3.726495e-02
## [1046] 3.833244e-02 4.046503e-02 4.128795e-02 4.161794e-02 4.169175e-02
## [1051] 4.232224e-02 4.236996e-02 4.282884e-02 4.427075e-02 4.428137e-02## alpha area
## 1 0.05751881 0.000000e+00
## 2 0.07104237 6.809045e-08
## 3 0.07929438 1.301971e-07
## 4 0.08378608 2.287676e-07
## 5 0.08510697 2.600994e-07
## 6 0.09448835 5.982050e-07p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)8 Ejemplo 4. Con la tabla de datos abalone.
8.1 Método de centros.
Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo abalone de RSDA. Se obtiene la matriz de centros asociada.
Sobre la matriz de centros, se aplica un modelo de regresión lineal clásico. Supongamos que se aplica un modelo de regresión lineal tomando como variable de respuesta Whole_Weight.
El modelo es: \(Y=-0.1834758-0.2693955X_{1}+1.4948113X_{2}+0.1146723X_{3}+0.6348267X_{4}+0.9660136X_{5}+0.8327747X_{6}\).
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
8.1.1 Contribución de la variable LENGTH al modelo de centros.
data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = LENGTH, y = Y.c))+geom_point()+labs(title = "LENGTH vs. Y") 
Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
modelo1 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "cm")
ypred1 <- sym.predict(modelo1, abalone)
ypred1$Fitted$Minimums <- round(ypred1$Fitted$Minimums, 2)
ypred1$Fitted$Maximums <- round(ypred1$Fitted$Maximums, 2)
length1 <- data.frame(lengthmin=c(0.28,0.30,0.34,0.39,0.40,0.45,0.49,0.55,0.08,0.13,0.26,0.32,0.34,0.44,0.45,0.16,0.16,0.20,0.29,0.35,0.42,0.49,0.52,0.60),lengthmax=c(0.66,0.74,0.78,0.82,0.74,0.80,0.72,0.70,0.24,0.58,0.67,0.66,0.72,0.65,0.58,0.21,0.53,0.72,0.78,0.76,0.78,0.74,0.69,0.66)) #variable LENGTH
clusters1 <- cbind(length1,ypred1$Fitted)
colnames(clusters1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1 <- ggplot() + geom_rect(data = clusters1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers for the variable LENGTH",
x = "LENGTH",
y = "Y"
) +
theme_minimal()
graf1 <- rectangulos1 +
geom_point(
data = clusters1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1 
Luego, se calcula el índice de bondad de ajuste geométrico.
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4## Estimating R2 Geom for variable = 5## Estimating R2 Geom for variable = 6
8.2 Método de centros y rangos.
Ahora, además de la matriz de centros se crea la matriz de rangos y se estudian los centros más rangos y los centros menos rangos.
data.r <- interval.ranges(data)
data.r <- round(data.r,2)
data.cmasr <- data.c + data.r
data.cmenosr <- data.c - data.rSe crea un modelo de regresión lineal clásico con los centros más rangos.
El modelo es \(Y=-0.19494+0.77978X_{1}-0.05459X_{2}+0.06312X_{3}+0.63785X_{4}+1.28787X_{5}+0.89348X_{6}\)
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
8.2.1 Contribución de la variable LENGTH al modelo de centros más rangos.
data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = LENGTH, y = Y.cmasr))+geom_point()+labs(title = "LENGTH vs. Y") #Nube de puntos LENGTH vs Y.cmasr
modelo2 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "crm")
ypred2 <- sym.predict(modelo2, abalone)
ypred2$Fitted$Minimums <- round(ypred2$Fitted$Minimums, 2)
ypred2$Fitted$Maximums <- round(ypred2$Fitted$Maximums, 2)
clusters2 <- cbind(length1,ypred2$Fitted)
colnames(clusters2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2 <- ggplot() + geom_rect(data = clusters2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable LENGTH", x="LENGTH",
y = "Y"
) +
theme_minimal()
graf2 <- rectangulos2 +
geom_point(
data = clusters2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4## Estimating R2 Geom for variable = 5## Estimating R2 Geom for variable = 6##
## Call:
## spatgeom_xy(x = x, y = y, scale = scale, nalphas = nalphas, envelope = envelope, mc_cores = mc_cores)
##
## Number of variables: 6
##
## Number of observations: 24
## # A tibble: 6 × 5
## variable_name mean_n intensity alpha geom_corr
## <chr> <dbl> <dbl> <fct> <fct>
## 1 DIAMETER 24 16.4 (0.034,0.697] (0.91,0.999]
## 2 HEIGHT 24 7.74 (0.0257,0.637] (0.777,1]
## 3 LENGTH 24 13.9 (0.0306,0.748] (0.912,1]
## 4 SHELL_WEIGHT 24 8.45 (0.0521,0.603] (0.879,1]
## 5 SHUCKED_WEIGHT 24 5.65 (0.0507,0.791] (0.909,1]
## 6 VISCERA_WEIGHT 24 11.1 (0.0404,0.444] (0.937,0.999]
Se repite lo anterior, pero ahora usando centros menos rangos.
El modelo es \(Y=-0.01563+1.11565X_{1}-1.39136X_{2}-0.05412X_{3}+0.30067X_{4}+1.70071X_{5}+1.77761X_{6}\)
8.2.2 Contribución de la variable LENGTH al modelo de centros menos rangos.
data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = LENGTH, y = Y.cmenosr))+geom_point()+labs(title = "LENGTH vs. Y") #Nube de puntos LENGTH vs Y.cmasr
modelo3 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "crm")
ypred3 <- sym.predict(modelo3, abalone)
ypred3$Fitted$Minimums <- round(ypred3$Fitted$Minimums,2)
ypred3$Fitted$Maximums <- round(ypred3$Fitted$Maximums,2)
clusters3 <- cbind(length1,ypred3$Fitted)
colnames(clusters3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3 <- ggplot() + geom_rect(data = clusters3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable LENGTH",
x = "LENGTH",
y = "Y"
) +
theme_minimal()
graf3 <- rectangulos3 +
geom_point(data = clusters3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4## Estimating R2 Geom for variable = 5## Estimating R2 Geom for variable = 6
8.2.3 Gráfica final para la variable LENGTH con el método de centros y rangos.
geom_indicesc <- indice1$results[[1]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[1]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicescmenosr <- indice3$results[[1]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()
# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
data_combined1 <- rbind(c(0,1),data_combined1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable Syst",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
## alpha.vals diff.geom_corr
## [1,] 0.01802776 0.0001120065
## [2,] 0.02236068 0.0007425235
## [3,] 0.02500000 0.0013730405
## [4,] 0.02692582 0.0013730405
## [5,] 0.02915476 0.0015306698
## [6,] 0.03162278 0.0016882990
## [7,] 0.03201562 0.0032645916
## [8,] 0.03201562 0.0032645916
## [9,] 0.03605551 0.0032808190
## [10,] 0.03640055 0.0034263714
## [11,] 0.03640055 0.0034263714
## [12,] 0.03905125 0.0040429249
## [13,] 0.04031129 0.0041564510
## [14,] 0.04031129 0.0041564510
## [15,] 0.04242641 0.0044860689
## [16,] 0.04716991 0.0057410552
## [17,] 0.04716991 0.0057410552
## [18,] 0.05000000 0.0047602901
## [19,] 0.06082763 0.0046183024
## [20,] 0.06403124 0.0027475600
## [21,] 0.06670832 0.0026580754
## [22,] 0.06946222 0.0070060729
## [23,] 0.07071068 0.0084096964
## [24,] 0.07158911 0.0083440835
## [25,] 0.07566373 0.0061061826
## [26,] 0.08000000 0.0031299895
## [27,] 0.08062258 0.0029436300
## [28,] 0.08544004 0.0036289790
## [29,] 0.09013878 0.0055382609
## [30,] 0.09013878 0.0055382609
## [31,] 0.09513149 0.0103554269
## [32,] 0.09552487 0.0104410471
## [33,] 0.09617692 0.0102122080
## [34,] 0.10000000 0.0111074824
## [35,] 0.10049876 0.0119487758
## [36,] 0.10124228 0.0134264555
## [37,] 0.10511898 0.0142874529
## [38,] 0.10793517 0.0143745133
## [39,] 0.11401754 0.0147249365
## [40,] 0.12539936 0.0170354227
## [41,] 0.12658989 0.0172764877
## [42,] 0.13536986 0.0195194870
## [43,] 0.13793114 0.0199042255
## [44,] 0.15074813 0.0186910880
## [45,] 0.16710775 0.0211025111
## [46,] 0.17066048 0.0221339335
## [47,] 0.17356555 0.0204585161
## [48,] 0.17464249 0.0200146978
## [49,] 0.17951323 0.0200584340
## [50,] 0.20099751 0.0269589484
## [51,] 0.22000000 0.0296404952
## [52,] 0.23505319 0.0335233383
## [53,] 0.23584953 0.0334318534
## [54,] 0.24135037 0.0373769500
## [55,] 0.24748737 0.0562651702
## [56,] 0.24839485 0.0594062508
## [57,] 0.29920729 0.0774123036
## [58,] 0.30008332 0.0777430629
## [59,] 0.31780497 0.0787324858
## [60,] 0.35510562 0.1191705005
## [61,] 0.36280160 0.1262083805
## [62,] 0.37406550 0.1280914689
## [63,] 0.47447339 0.1649297176
## [64,] 0.48703183 0.1673596859
## [65,] 0.58860003 0.1923946039
## [66,] 0.65370100 0.2076077809
## [67,] 1.06894808 0.1436509645
## [68,] 1.36792726 0.1272456219
## [69,] 1.46400990 0.1202479448
## [1] 0.000000e+00 3.217297e-06 6.841191e-06 9.485426e-06 1.289719e-05
## [6] 1.706394e-05 1.834642e-05 1.834642e-05 3.160057e-05 3.278279e-05
## [11] 3.278279e-05 4.349937e-05 4.873667e-05 4.873667e-05 5.822523e-05
## [16] 8.545792e-05 8.545792e-05 9.892999e-05 1.489352e-04 1.577374e-04
## [21] 1.648532e-04 1.841473e-04 1.946464e-04 2.019761e-04 2.268565e-04
## [26] 2.404290e-04 2.422616e-04 2.597441e-04 2.857669e-04 2.857669e-04
## [31] 3.374685e-04 3.415758e-04 3.482347e-04 3.906995e-04 3.966591e-04
## [36] 4.066420e-04 4.620301e-04 5.025114e-04 5.920740e-04 7.859681e-04
## [41] 8.065363e-04 9.779169e-04 1.028897e-03 1.268461e-03 1.613690e-03
## [46] 1.692326e-03 1.751759e-03 1.773314e-03 1.871013e-03 2.450207e-03
## [51] 3.013450e-03 3.518083e-03 3.544706e-03 3.750311e-03 4.095610e-03
## [56] 4.149520e-03 8.083028e-03 8.151134e-03 9.546403e-03 1.399154e-02
## [61] 1.496284e-02 1.640565e-02 3.296589e-02 3.506767e-02 5.460884e-02
## [66] 6.812431e-02 1.277750e-01 1.658187e-01 1.773725e-01## alpha area
## 1 0.01802776 0.000000e+00
## 2 0.02236068 3.217297e-06
## 3 0.02500000 6.841191e-06
## 4 0.02692582 9.485426e-06
## 5 0.02915476 1.289719e-05
## 6 0.03162278 1.706394e-05
## 7 0.03201562 1.834642e-05
## 8 0.03201562 1.834642e-05
## 9 0.03605551 3.160057e-05
## 10 0.03640055 3.278279e-05
## 11 0.03640055 3.278279e-05
## 12 0.03905125 4.349937e-05
## 13 0.04031129 4.873667e-05
## 14 0.04031129 4.873667e-05
## 15 0.04242641 5.822523e-05
## 16 0.04716991 8.545792e-05
## 17 0.04716991 8.545792e-05
## 18 0.05000000 9.892999e-05
## 19 0.06082763 1.489352e-04
## 20 0.06403124 1.577374e-04
## 21 0.06670832 1.648532e-04
## 22 0.06946222 1.841473e-04
## 23 0.07071068 1.946464e-04
## 24 0.07158911 2.019761e-04
## 25 0.07566373 2.268565e-04
## 26 0.08000000 2.404290e-04
## 27 0.08062258 2.422616e-04
## 28 0.08544004 2.597441e-04
## 29 0.09013878 2.857669e-04
## 30 0.09013878 2.857669e-04
## 31 0.09513149 3.374685e-04
## 32 0.09552487 3.415758e-04
## 33 0.09617692 3.482347e-04
## 34 0.10000000 3.906995e-04
## 35 0.10049876 3.966591e-04
## 36 0.10124228 4.066420e-04
## 37 0.10511898 4.620301e-04
## 38 0.10793517 5.025114e-04
## 39 0.11401754 5.920740e-04
## 40 0.12539936 7.859681e-04
## 41 0.12658989 8.065363e-04
## 42 0.13536986 9.779169e-04
## 43 0.13793114 1.028897e-03
## 44 0.15074813 1.268461e-03
## 45 0.16710775 1.613690e-03
## 46 0.17066048 1.692326e-03
## 47 0.17356555 1.751759e-03
## 48 0.17464249 1.773314e-03
## 49 0.17951323 1.871013e-03
## 50 0.20099751 2.450207e-03
## 51 0.22000000 3.013450e-03
## 52 0.23505319 3.518083e-03
## 53 0.23584953 3.544706e-03
## 54 0.24135037 3.750311e-03
## 55 0.24748737 4.095610e-03
## 56 0.24839485 4.149520e-03
## 57 0.29920729 8.083028e-03
## 58 0.30008332 8.151134e-03
## 59 0.31780497 9.546403e-03
## 60 0.35510562 1.399154e-02
## 61 0.36280160 1.496284e-02
## 62 0.37406550 1.640565e-02
## 63 0.47447339 3.296589e-02
## 64 0.48703183 3.506767e-02
## 65 0.58860003 5.460884e-02
## 66 0.65370100 6.812431e-02
## 67 1.06894808 1.277750e-01
## 68 1.36792726 1.658187e-01
## 69 1.46400990 1.773725e-01p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)8.2.4 Contribución de la variable DIAMETER al modelo de centros.
data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = DIAMETER, y = Y.c))+geom_point()+labs(title = "LENGTH vs. Y") 
Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
diameter1 <- data.frame(lengthmin=c(0.20,0.22,0.26,0.30,0.32,0.38,0.36,0.46,0.06,0.10,0.20,0.24,0.26,0.33,0.36,0.11,0.12,0.16,0.22,0.26,0.32,0.38,0.40,0.50),lengthmax=c(0.48,0.58,0.63,0.65,0.60,0.63,0.58,0.58,0.18,0.45,0.50,0.52,0.55,0.52,0.44,0.15,0.41,0.57,0.63,0.60,0.59,0.59,0.54,0.54)) #variable DIAMETER
clusters1.1 <- cbind(diameter1,ypred1$Fitted)
colnames(clusters1.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.1 <- ggplot() + geom_rect(data = clusters1.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable DIAMETER",
x = "DIAMETER",
y = "Y"
) +
theme_minimal()
graf1.1 <- rectangulos1.1 +
geom_point(
data = clusters1.1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.1
8.2.5 Contribución de la variable DIAMETER al modelo de centros más rangos.
data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = DIAMETER, y = Y.cmasr))+geom_point()+labs(title = "DIAMETER vs. Y") 
clusters2.1 <- cbind(diameter1,ypred2$Fitted)
colnames(clusters2.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.1 <- ggplot() + geom_rect(data = clusters2.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable DIAMETER", x="DIAMETER",
y = "Y"
) +
theme_minimal()
graf2.1 <- rectangulos2.1 +
geom_point(
data = clusters2.1,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.1
8.2.6 Contribución de la variable DIAMETER al modelo de centros menos rangos.
data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = DIAMETER, y = Y.cmenosr))+geom_point()+labs(title = "DIAMETER vs. Y") 
clusters3.1 <- cbind(diameter1,ypred3$Fitted)
colnames(clusters3.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.1 <- ggplot() + geom_rect(data = clusters3.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Point clouds of centers and extremes",
x = "Variable 1",
y = "Y"
) +
theme_minimal()
graf3.1 <- rectangulos3.1 +
geom_point(data = clusters3.1,
aes(x = lengthmin, y = ymin),
color = "green", size = 2, alpha = 0.9
)+ geom_point(
data = clusters2.1,
aes(x = lengthmax, y = ymax),
color = "red", size = 2, alpha = 0.9
)+
geom_point(
data = clusters1.1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf3.1
8.2.7 Gráfica final para la variable DIAMETER con el método de centros y rangos.
geom_indicesc <- indice1$results[[2]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[2]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicescmenosr <- indice3$results[[2]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()
# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable DIAMETER",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
## alpha.vals diff.geom_corr
## [1,] 0.01414214 -5.010507e-04
## [2,] 0.02061553 -4.567734e-05
## [3,] 0.02236068 -4.567734e-05
## [4,] 0.02236068 1.411518e-03
## [5,] 0.02500000 1.957966e-03
## [6,] 0.02500000 3.141937e-03
## [7,] 0.03162278 3.506235e-03
## [8,] 0.03162278 3.870534e-03
## [9,] 0.03162278 3.870534e-03
## [10,] 0.03354102 5.236654e-03
## [11,] 0.03535534 5.893799e-03
## [12,] 0.03605551 6.137749e-03
## [13,] 0.03605551 6.502047e-03
## [14,] 0.04031129 6.625529e-03
## [15,] 0.04031129 6.625529e-03
## [16,] 0.04123106 5.972963e-03
## [17,] 0.04472136 6.908696e-03
## [18,] 0.05000000 6.864848e-03
## [19,] 0.05315073 6.191568e-03
## [20,] 0.06020797 5.830334e-03
## [21,] 0.06184658 5.160336e-03
## [22,] 0.06324555 5.031947e-03
## [23,] 0.06403124 7.339810e-03
## [24,] 0.06576473 7.989346e-03
## [25,] 0.07071068 6.842667e-03
## [26,] 0.07648529 5.925128e-03
## [27,] 0.08000000 5.716900e-03
## [28,] 0.08062258 5.481027e-03
## [29,] 0.08246211 4.802202e-03
## [30,] 0.08845903 3.382224e-03
## [31,] 0.08860023 7.694121e-03
## [32,] 0.09013878 7.944798e-03
## [33,] 0.09055385 7.368050e-03
## [34,] 0.09219544 8.056195e-03
## [35,] 0.09513149 8.818497e-03
## [36,] 0.09617692 9.029980e-03
## [37,] 0.09708244 7.937025e-03
## [38,] 0.09823441 8.433267e-03
## [39,] 0.10688779 9.048712e-03
## [40,] 0.10770330 7.136662e-03
## [41,] 0.11011358 6.400595e-03
## [42,] 0.11101802 6.303947e-03
## [43,] 0.12257651 9.113461e-03
## [44,] 0.12539936 8.407843e-03
## [45,] 0.12747549 8.599094e-03
## [46,] 0.13583078 8.581774e-03
## [47,] 0.14849242 1.020693e-02
## [48,] 0.15000000 1.041223e-02
## [49,] 0.17029386 1.228544e-02
## [50,] 0.17117243 1.034592e-02
## [51,] 0.17182840 8.070621e-03
## [52,] 0.20000000 1.324926e-02
## [53,] 0.22022716 1.688006e-02
## [54,] 0.23021729 1.902845e-02
## [55,] 0.23632605 4.224508e-02
## [56,] 0.23690715 4.435955e-02
## [57,] 0.24253866 5.200286e-02
## [58,] 0.24682990 5.182597e-02
## [59,] 0.26800187 5.372343e-02
## [60,] 0.27771388 4.965851e-02
## [61,] 0.29652150 5.272071e-02
## [62,] 0.29920729 5.267673e-02
## [63,] 0.31184932 5.238803e-02
## [64,] 0.31894357 5.227292e-02
## [65,] 0.34179672 7.759101e-02
## [66,] 0.35106979 8.887216e-02
## [67,] 0.46671726 1.219334e-01
## [68,] 0.64352545 1.702145e-01
## [69,] 0.69146583 1.654053e-01
## [70,] 0.72292807 1.623309e-01
## [71,] 1.06303810 1.217147e-01
## [72,] 1.35875862 8.594917e-02
## [1] 0.000000e+00 -2.956874e-07 -3.754012e-07 -3.754012e-07 4.792297e-06
## [6] 4.792297e-06 2.801331e-05 2.801331e-05 2.801331e-05 3.805849e-05
## [11] 4.875172e-05 5.304921e-05 5.304921e-05 8.124598e-05 8.124598e-05
## [16] 8.673971e-05 1.108532e-04 1.470902e-04 1.665982e-04 2.077443e-04
## [21] 2.162000e-04 2.232396e-04 2.290064e-04 2.428558e-04 2.766993e-04
## [26] 3.109146e-04 3.310079e-04 3.344202e-04 3.432541e-04 3.635370e-04
## [31] 3.646233e-04 3.768469e-04 3.799051e-04 3.931301e-04 4.190216e-04
## [36] 4.284618e-04 4.356490e-04 4.453639e-04 5.236658e-04 5.294858e-04
## [41] 5.449130e-04 5.506146e-04 6.559524e-04 6.796865e-04 6.975393e-04
## [46] 7.692425e-04 8.984790e-04 9.141762e-04 1.163495e-03 1.172585e-03
## [51] 1.177879e-03 1.551132e-03 1.892567e-03 2.082664e-03 2.340729e-03
## [56] 2.366507e-03 2.659361e-03 2.881759e-03 4.019189e-03 4.501474e-03
## [61] 5.493025e-03 5.634503e-03 6.296794e-03 6.667631e-03 8.440831e-03
## [66] 9.264949e-03 2.336624e-02 5.346155e-02 6.139115e-02 6.649844e-02
## [71] 1.078948e-01 1.333118e-01## alpha area
## 1 0.01414214 0.000000e+00
## 2 0.02061553 -2.956874e-07
## 3 0.02236068 -3.754012e-07
## 4 0.02236068 -3.754012e-07
## 5 0.02500000 4.792297e-06
## 6 0.02500000 4.792297e-06
## 7 0.03162278 2.801331e-05
## 8 0.03162278 2.801331e-05
## 9 0.03162278 2.801331e-05
## 10 0.03354102 3.805849e-05
## 11 0.03535534 4.875172e-05
## 12 0.03605551 5.304921e-05
## 13 0.03605551 5.304921e-05
## 14 0.04031129 8.124598e-05
## 15 0.04031129 8.124598e-05
## 16 0.04123106 8.673971e-05
## 17 0.04472136 1.108532e-04
## 18 0.05000000 1.470902e-04
## 19 0.05315073 1.665982e-04
## 20 0.06020797 2.077443e-04
## 21 0.06184658 2.162000e-04
## 22 0.06324555 2.232396e-04
## 23 0.06403124 2.290064e-04
## 24 0.06576473 2.428558e-04
## 25 0.07071068 2.766993e-04
## 26 0.07648529 3.109146e-04
## 27 0.08000000 3.310079e-04
## 28 0.08062258 3.344202e-04
## 29 0.08246211 3.432541e-04
## 30 0.08845903 3.635370e-04
## 31 0.08860023 3.646233e-04
## 32 0.09013878 3.768469e-04
## 33 0.09055385 3.799051e-04
## 34 0.09219544 3.931301e-04
## 35 0.09513149 4.190216e-04
## 36 0.09617692 4.284618e-04
## 37 0.09708244 4.356490e-04
## 38 0.09823441 4.453639e-04
## 39 0.10688779 5.236658e-04
## 40 0.10770330 5.294858e-04
## 41 0.11011358 5.449130e-04
## 42 0.11101802 5.506146e-04
## 43 0.12257651 6.559524e-04
## 44 0.12539936 6.796865e-04
## 45 0.12747549 6.975393e-04
## 46 0.13583078 7.692425e-04
## 47 0.14849242 8.984790e-04
## 48 0.15000000 9.141762e-04
## 49 0.17029386 1.163495e-03
## 50 0.17117243 1.172585e-03
## 51 0.17182840 1.177879e-03
## 52 0.20000000 1.551132e-03
## 53 0.22022716 1.892567e-03
## 54 0.23021729 2.082664e-03
## 55 0.23632605 2.340729e-03
## 56 0.23690715 2.366507e-03
## 57 0.24253866 2.659361e-03
## 58 0.24682990 2.881759e-03
## 59 0.26800187 4.019189e-03
## 60 0.27771388 4.501474e-03
## 61 0.29652150 5.493025e-03
## 62 0.29920729 5.634503e-03
## 63 0.31184932 6.296794e-03
## 64 0.31894357 6.667631e-03
## 65 0.34179672 8.440831e-03
## 66 0.35106979 9.264949e-03
## 67 0.46671726 2.336624e-02
## 68 0.64352545 5.346155e-02
## 69 0.69146583 6.139115e-02
## 70 0.72292807 6.649844e-02
## 71 1.06303810 1.078948e-01
## 72 1.35875862 1.333118e-01p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)8.2.8 Contribución de la variable HEIGHT al modelo de centros.
data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = HEIGHT, y = Y.c))+geom_point()+labs(title = "HEIGHT vs. Y") 
Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
height1 <- data.frame(lengthmin=c(0.07,0.02,0.06,0.10,0.10,0.14,0.12,0.18,0.01,0.00,0.00,0.08,0.08,0.12,0.12,0.04,0.02,0.04,0.06,0.08,0.12,0.13,0.14,0.20),lengthmax=c(0.18,1.13,0.23,0.25,0.24,0.22,0.21,0.22,0.06,0.15,0.18,0.19,0.22,0.20,0.18,0.05,0.16,0.20,0.52,0.24,0.24,0.23,0.22,0.22)) #variable HEIGHT
clusters1.2 <- cbind(height1,ypred1$Fitted)
colnames(clusters1.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.2 <- ggplot() + geom_rect(data = clusters1.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf1.2 <- rectangulos1.2 +
geom_point(
data = clusters1.2,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.2 
8.2.9 Contribución de la variable HEIGHT al modelo de centros más rangos.
data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = HEIGHT, y = Y.cmasr))+geom_point()+labs(title = "HEIGHT vs. Y") 
clusters2.2 <- cbind(height1,ypred2$Fitted)
colnames(clusters2.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.2 <- ggplot() + geom_rect(data = clusters2.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable HEIGHT", x="HEIGHT",
y = "Y"
) +
theme_minimal()
graf2.2 <- rectangulos2.2 +
geom_point(
data = clusters2.2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.2
8.2.10 Contribución de la variable HEIGHT al modelo de centros menos rangos.
data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = HEIGHT, y = Y.cmenosr))+geom_point()+labs(title = "DIAMETER vs. Y") 
clusters3.2 <- cbind(height1,ypred3$Fitted)
colnames(clusters3.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.2 <- ggplot() + geom_rect(data = clusters3.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf3.2 <- rectangulos3.2 +
geom_point(data = clusters3.2,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3.2
8.2.11 Gráfica final para la variable HEIGHT con el método de centros y rangos.
geom_indicesc <- indice1$results[[3]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[3]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicescmenosr <- indice3$results[[3]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()
# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable HEIGHT",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
## alpha.vals diff.geom_corr
## [1,] 0.01414214 0.0007228854
## [2,] 0.01500000 0.0019523936
## [3,] 0.02000000 0.0019523936
## [4,] 0.02061553 0.0027720658
## [5,] 0.02061553 0.0035917379
## [6,] 0.02236068 0.0048212461
## [7,] 0.02500000 0.0056409182
## [8,] 0.02692582 0.0073093740
## [9,] 0.03162278 0.0113322618
## [10,] 0.03162278 0.0129716061
## [11,] 0.03162278 0.0129716061
## [12,] 0.03500000 0.0186759760
## [13,] 0.03535534 0.0203118129
## [14,] 0.03640055 0.0280883814
## [15,] 0.03807887 0.0372931270
## [16,] 0.04000000 0.0382732793
## [17,] 0.04031129 0.0383061208
## [18,] 0.04123106 0.0387814770
## [19,] 0.04609772 0.0451181535
## [20,] 0.06020797 0.0475314107
## [21,] 0.06020797 0.0475314107
## [22,] 0.06324555 0.0501857712
## [23,] 0.06576473 0.0524705353
## [24,] 0.07071068 0.0527812704
## [25,] 0.07566373 0.0529299117
## [26,] 0.07648529 0.0529920638
## [27,] 0.08062258 0.0561948328
## [28,] 0.08631338 0.0607669036
## [29,] 0.09055385 0.0617632425
## [30,] 0.09552487 0.0626457139
## [31,] 0.10111874 0.0648797609
## [32,] 0.10198039 0.0649591454
## [33,] 0.10511898 0.0651813762
## [34,] 0.10606602 0.0655987524
## [35,] 0.11011358 0.0662024758
## [36,] 0.11543396 0.0670859265
## [37,] 0.12093387 0.0674891073
## [38,] 0.12539936 0.0676579870
## [39,] 0.12589678 0.0700949015
## [40,] 0.12816006 0.0865926981
## [41,] 0.13509256 0.0874349083
## [42,] 0.15033296 0.0897377629
## [43,] 0.17334936 0.0932501557
## [44,] 0.17507141 0.0913904413
## [45,] 0.18027756 0.0915444775
## [46,] 0.18560711 0.0917189880
## [47,] 0.19448650 0.0895788887
## [48,] 0.20886599 0.0901580500
## [49,] 0.21708293 0.0905918177
## [50,] 0.23584953 0.1208457877
## [51,] 0.25223997 0.1503439841
## [52,] 0.26076810 0.1521643056
## [53,] 0.31184932 0.1672753412
## [54,] 0.33000000 0.1745228845
## [55,] 0.34234486 0.1795039584
## [56,] 0.45024993 0.2163580680
## [57,] 0.45400991 0.1464426057
## [58,] 0.46010868 0.1191031189
## [59,] 0.46270941 0.0942506732
## [60,] 0.47055818 0.0887193863
## [61,] 0.50982840 0.0708803823
## [62,] 0.53956001 0.0642094976
## [63,] 0.54664888 0.0655506576
## [64,] 0.56678920 0.0656735804
## [65,] 0.57212324 0.0659928611
## [66,] 0.59076222 0.0636600651
## [67,] 0.61459336 0.0380438565
## [68,] 0.63780875 0.0301073486
## [69,] 0.76134749 -0.0254482070
## [70,] 0.82602966 -0.0411437806
## [71,] 1.21652168 -0.1599333018
## [72,] 1.24788822 -0.1631272623
## [1] 0.000000e+00 1.674889e-06 1.143686e-05 1.314314e-05 1.314314e-05
## [6] 2.155695e-05 3.644514e-05 5.052171e-05 1.037488e-04 1.037488e-04
## [11] 1.037488e-04 1.668217e-04 1.740393e-04 2.033976e-04 2.659872e-04
## [16] 3.395154e-04 3.514396e-04 3.871096e-04 6.066846e-04 1.277365e-03
## [21] 1.277365e-03 1.429808e-03 1.561991e-03 1.823044e-03 2.085209e-03
## [26] 2.128745e-03 2.361239e-03 2.707051e-03 2.968957e-03 3.280369e-03
## [31] 3.643299e-03 3.699271e-03 3.903848e-03 3.965973e-03 4.233931e-03
## [36] 4.590854e-03 4.962038e-03 5.264164e-03 5.299031e-03 5.495014e-03
## [41] 6.101157e-03 7.468796e-03 9.615079e-03 9.772458e-03 1.024905e-02
## [46] 1.073787e-02 1.153328e-02 1.282971e-02 1.357409e-02 1.584196e-02
## [51] 1.830616e-02 1.960384e-02 2.814847e-02 3.131618e-02 3.353213e-02
## [56] 5.687826e-02 5.742888e-02 5.815526e-02 5.840038e-02 5.909672e-02
## [61] 6.188021e-02 6.378926e-02 6.425394e-02 6.557663e-02 6.592864e-02
## [66] 6.711520e-02 6.802183e-02 6.872078e-02 6.557694e-02 6.291567e-02
## [71] 4.629927e-04 -4.653744e-03## alpha area
## 1 0.01414214 0.000000e+00
## 2 0.01500000 1.674889e-06
## 3 0.02000000 1.143686e-05
## 4 0.02061553 1.314314e-05
## 5 0.02061553 1.314314e-05
## 6 0.02236068 2.155695e-05
## 7 0.02500000 3.644514e-05
## 8 0.02692582 5.052171e-05
## 9 0.03162278 1.037488e-04
## 10 0.03162278 1.037488e-04
## 11 0.03162278 1.037488e-04
## 12 0.03500000 1.668217e-04
## 13 0.03535534 1.740393e-04
## 14 0.03640055 2.033976e-04
## 15 0.03807887 2.659872e-04
## 16 0.04000000 3.395154e-04
## 17 0.04031129 3.514396e-04
## 18 0.04123106 3.871096e-04
## 19 0.04609772 6.066846e-04
## 20 0.06020797 1.277365e-03
## 21 0.06020797 1.277365e-03
## 22 0.06324555 1.429808e-03
## 23 0.06576473 1.561991e-03
## 24 0.07071068 1.823044e-03
## 25 0.07566373 2.085209e-03
## 26 0.07648529 2.128745e-03
## 27 0.08062258 2.361239e-03
## 28 0.08631338 2.707051e-03
## 29 0.09055385 2.968957e-03
## 30 0.09552487 3.280369e-03
## 31 0.10111874 3.643299e-03
## 32 0.10198039 3.699271e-03
## 33 0.10511898 3.903848e-03
## 34 0.10606602 3.965973e-03
## 35 0.11011358 4.233931e-03
## 36 0.11543396 4.590854e-03
## 37 0.12093387 4.962038e-03
## 38 0.12539936 5.264164e-03
## 39 0.12589678 5.299031e-03
## 40 0.12816006 5.495014e-03
## 41 0.13509256 6.101157e-03
## 42 0.15033296 7.468796e-03
## 43 0.17334936 9.615079e-03
## 44 0.17507141 9.772458e-03
## 45 0.18027756 1.024905e-02
## 46 0.18560711 1.073787e-02
## 47 0.19448650 1.153328e-02
## 48 0.20886599 1.282971e-02
## 49 0.21708293 1.357409e-02
## 50 0.23584953 1.584196e-02
## 51 0.25223997 1.830616e-02
## 52 0.26076810 1.960384e-02
## 53 0.31184932 2.814847e-02
## 54 0.33000000 3.131618e-02
## 55 0.34234486 3.353213e-02
## 56 0.45024993 5.687826e-02
## 57 0.45400991 5.742888e-02
## 58 0.46010868 5.815526e-02
## 59 0.46270941 5.840038e-02
## 60 0.47055818 5.909672e-02
## 61 0.50982840 6.188021e-02
## 62 0.53956001 6.378926e-02
## 63 0.54664888 6.425394e-02
## 64 0.56678920 6.557663e-02
## 65 0.57212324 6.592864e-02
## 66 0.59076222 6.711520e-02
## 67 0.61459336 6.802183e-02
## 68 0.63780875 6.872078e-02
## 69 0.76134749 6.557694e-02
## 70 0.82602966 6.291567e-02
## 71 1.21652168 4.629927e-04
## 72 1.24788822 -4.653744e-03p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada) 8.2.12 Contribución de la variable SHUCKED_WEIGHT al modelo de centros.
data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = SHUCKED_WEIGHT, y = Y.c))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") 
Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
shucked_weight1 <- data.frame(lengthmin=c(0.03,0.06,0.07,0.11,0.12,0.16,0.16,0.32,0.00,0.00,0.03,0.06,0.07,0.16,0.11,0.01,0.01,0.02,0.04,0.10,0.11,0.22,0.25,0.38),lengthmax=c(0.64,1.16,1.49,1.23,0.84,0.93,0.82,0.71,0.03,0.50,0.60,0.72,0.77,0.63,0.39,0.02,0.32,1.25,1.35,1.35,1.15,0.87,0.74,0.75)) #variable SHUCKED_WEIGHT
clusters1.3 <- cbind(shucked_weight1,ypred1$Fitted)
colnames(clusters1.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.3 <- ggplot() + geom_rect(data = clusters1.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf1.3 <- rectangulos1.3 +
geom_point(
data = clusters1.3,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.3
8.2.13 Contribución de la variable SHUCKED_WEIGHT al modelo de centros más rangos.
data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = SHUCKED_WEIGHT, y = Y.cmasr))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") 
clusters2.3 <- cbind(shucked_weight1,ypred2$Fitted)
colnames(clusters2.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.3 <- ggplot() + geom_rect(data = clusters2.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable SHUCKED_WEIGHT ", x="SHUCKED_WEIGHT",
y = "Y"
) +
theme_minimal()
graf2.3 <- rectangulos2.3 +
geom_point(
data = clusters2.3,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.3
8.2.14 Contribución de la variable SHUCKED_WEIGHT al modelo de centros menos rangos.
data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = SHUCKED_WEIGHT, y = Y.cmenosr))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") 
clusters3.3 <- cbind(shucked_weight1,ypred3$Fitted)
colnames(clusters3.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.3 <- ggplot() + geom_rect(data = clusters3.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable SHUCKED_WEIGHT ",
x = "SHUCKED_WEIGHT",
y = "Y"
) +
theme_minimal()
graf3.3 <- rectangulos3.3 +
geom_point(data = clusters3.3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3.3
8.2.15 Gráfica final para la variable SHUCKED_WEIGHT con el método de centros y rangos.
geom_indicesc <- indice1$results[[4]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[4]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicescmenosr <- indice3$results[[4]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()
# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable SHUCKED_WEIGHT",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
## alpha.vals diff.geom_corr
## [1,] 0.01118034 -6.056878e-05
## [2,] 0.01118034 1.496036e-04
## [3,] 0.01581139 4.648621e-04
## [4,] 0.02061553 8.852068e-04
## [5,] 0.02236068 1.095379e-03
## [6,] 0.02500000 2.356413e-03
## [7,] 0.02828427 3.617447e-03
## [8,] 0.03041381 4.247964e-03
## [9,] 0.03201562 6.980205e-03
## [10,] 0.03640055 7.610722e-03
## [11,] 0.03640055 8.031066e-03
## [12,] 0.03640055 8.031066e-03
## [13,] 0.03807887 8.136153e-03
## [14,] 0.04031129 8.661583e-03
## [15,] 0.04031129 9.081928e-03
## [16,] 0.04272002 9.607359e-03
## [17,] 0.04272002 9.607359e-03
## [18,] 0.04924429 1.065822e-02
## [19,] 0.05220153 1.089162e-02
## [20,] 0.05590170 1.071911e-02
## [21,] 0.05852350 1.123065e-02
## [22,] 0.06082763 1.114648e-02
## [23,] 0.06324555 1.130882e-02
## [24,] 0.06519202 1.263236e-02
## [25,] 0.07158911 1.331490e-02
## [26,] 0.07500000 1.323167e-02
## [27,] 0.07905694 1.786537e-02
## [28,] 0.08062258 2.855482e-02
## [29,] 0.08544004 3.174775e-02
## [30,] 0.08732125 3.311988e-02
## [31,] 0.09823441 4.825552e-02
## [32,] 0.09962429 4.866091e-02
## [33,] 0.10124228 6.144676e-02
## [34,] 0.10547512 6.159465e-02
## [35,] 0.10700467 6.074432e-02
## [36,] 0.11101802 5.880626e-02
## [37,] 0.11423660 5.785719e-02
## [38,] 0.11672618 5.934314e-02
## [39,] 0.11800424 5.890536e-02
## [40,] 0.12649111 5.811779e-02
## [41,] 0.13509256 5.768003e-02
## [42,] 0.14534442 5.560988e-02
## [43,] 0.14773287 5.278407e-02
## [44,] 0.15231546 5.067310e-02
## [45,] 0.15508062 4.303702e-02
## [46,] 0.16807736 3.837919e-02
## [47,] 0.17528548 3.217680e-02
## [48,] 0.17585505 2.419068e-02
## [49,] 0.17951323 2.276585e-02
## [50,] 0.18027756 2.248352e-02
## [51,] 0.18445867 2.089791e-02
## [52,] 0.19300259 1.707275e-02
## [53,] 0.20081086 1.635015e-02
## [54,] 0.20892582 1.740634e-02
## [55,] 0.21708293 1.600091e-02
## [56,] 0.22051077 2.126034e-02
## [57,] 0.23264780 4.280093e-02
## [58,] 0.23837995 5.320202e-02
## [59,] 0.24382371 6.146205e-02
## [60,] 0.24824383 6.883527e-02
## [61,] 0.30269622 9.753402e-02
## [62,] 0.30700163 9.446121e-02
## [63,] 0.30809901 9.303622e-02
## [64,] 0.33678628 8.478450e-02
## [65,] 0.37202150 7.965219e-02
## [66,] 0.42323162 7.640330e-02
## [67,] 0.54362211 6.764541e-02
## [68,] 0.54555018 6.349012e-02
## [69,] 0.58234440 5.344916e-02
## [70,] 0.61386073 5.271933e-02
## [71,] 0.62325757 5.016495e-02
## [72,] 0.70178344 4.595081e-02
## [73,] 0.79851425 4.113632e-02
## [74,] 1.31088710 6.716886e-03
## [75,] 1.53075145 -4.536528e-03
## [1] 0.000000e+00 2.595208e-22 2.152799e-06 6.405456e-06 8.317058e-06
## [6] 1.453639e-05 2.641707e-05 3.546328e-05 4.664423e-05 8.001670e-05
## [11] 8.001670e-05 8.001670e-05 9.367174e-05 1.130081e-04 1.130081e-04
## [16] 1.361496e-04 1.361496e-04 2.056867e-04 2.378959e-04 2.775584e-04
## [21] 3.070029e-04 3.326858e-04 3.600297e-04 3.846182e-04 4.697947e-04
## [26] 5.149266e-04 5.874053e-04 6.321118e-04 7.850553e-04 8.473607e-04
## [31] 1.373981e-03 1.441614e-03 1.541034e-03 1.801754e-03 1.894666e-03
## [36] 2.130676e-03 2.316894e-03 2.464633e-03 2.539918e-03 3.033156e-03
## [41] 3.529288e-03 4.099393e-03 4.225465e-03 4.457679e-03 4.576683e-03
## [46] 5.075488e-03 5.307422e-03 5.321200e-03 5.404482e-03 5.421667e-03
## [51] 5.509043e-03 5.654911e-03 5.782578e-03 5.923829e-03 6.054351e-03
## [56] 6.127228e-03 6.646704e-03 6.951666e-03 7.286250e-03 7.590511e-03
## [61] 1.290147e-02 1.330817e-02 1.341026e-02 1.584250e-02 1.864906e-02
## [66] 2.256168e-02 3.070555e-02 3.082796e-02 3.279458e-02 3.445610e-02
## [71] 3.492749e-02 3.853582e-02 4.251497e-02 4.595652e-02 4.495910e-02## alpha area
## 1 0.01118034 0.000000e+00
## 2 0.01118034 2.595208e-22
## 3 0.01581139 2.152799e-06
## 4 0.02061553 6.405456e-06
## 5 0.02236068 8.317058e-06
## 6 0.02500000 1.453639e-05
## 7 0.02828427 2.641707e-05
## 8 0.03041381 3.546328e-05
## 9 0.03201562 4.664423e-05
## 10 0.03640055 8.001670e-05
## 11 0.03640055 8.001670e-05
## 12 0.03640055 8.001670e-05
## 13 0.03807887 9.367174e-05
## 14 0.04031129 1.130081e-04
## 15 0.04031129 1.130081e-04
## 16 0.04272002 1.361496e-04
## 17 0.04272002 1.361496e-04
## 18 0.04924429 2.056867e-04
## 19 0.05220153 2.378959e-04
## 20 0.05590170 2.775584e-04
## 21 0.05852350 3.070029e-04
## 22 0.06082763 3.326858e-04
## 23 0.06324555 3.600297e-04
## 24 0.06519202 3.846182e-04
## 25 0.07158911 4.697947e-04
## 26 0.07500000 5.149266e-04
## 27 0.07905694 5.874053e-04
## 28 0.08062258 6.321118e-04
## 29 0.08544004 7.850553e-04
## 30 0.08732125 8.473607e-04
## 31 0.09823441 1.373981e-03
## 32 0.09962429 1.441614e-03
## 33 0.10124228 1.541034e-03
## 34 0.10547512 1.801754e-03
## 35 0.10700467 1.894666e-03
## 36 0.11101802 2.130676e-03
## 37 0.11423660 2.316894e-03
## 38 0.11672618 2.464633e-03
## 39 0.11800424 2.539918e-03
## 40 0.12649111 3.033156e-03
## 41 0.13509256 3.529288e-03
## 42 0.14534442 4.099393e-03
## 43 0.14773287 4.225465e-03
## 44 0.15231546 4.457679e-03
## 45 0.15508062 4.576683e-03
## 46 0.16807736 5.075488e-03
## 47 0.17528548 5.307422e-03
## 48 0.17585505 5.321200e-03
## 49 0.17951323 5.404482e-03
## 50 0.18027756 5.421667e-03
## 51 0.18445867 5.509043e-03
## 52 0.19300259 5.654911e-03
## 53 0.20081086 5.782578e-03
## 54 0.20892582 5.923829e-03
## 55 0.21708293 6.054351e-03
## 56 0.22051077 6.127228e-03
## 57 0.23264780 6.646704e-03
## 58 0.23837995 6.951666e-03
## 59 0.24382371 7.286250e-03
## 60 0.24824383 7.590511e-03
## 61 0.30269622 1.290147e-02
## 62 0.30700163 1.330817e-02
## 63 0.30809901 1.341026e-02
## 64 0.33678628 1.584250e-02
## 65 0.37202150 1.864906e-02
## 66 0.42323162 2.256168e-02
## 67 0.54362211 3.070555e-02
## 68 0.54555018 3.082796e-02
## 69 0.58234440 3.279458e-02
## 70 0.61386073 3.445610e-02
## 71 0.62325757 3.492749e-02
## 72 0.70178344 3.853582e-02
## 73 0.79851425 4.251497e-02
## 74 1.31088710 4.595652e-02
## 75 1.53075145 4.495910e-02p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada) # Esta curva coincide con la nube de puntos de las diferencias, puesto que es la derivada de la curva obtenida con integración. El máximo alpha obtenido es 0.39HACER LO MISMO CON TODAS LAS OTRAS VARIABLES.
9 Ejemplo 2. Con la tabla de datos simbólica cardiologicalv2.
9.1 Método de centros.
Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo cardiologicalv2 de RSDA.
Se obtiene la matriz de centros asociada.
Sobre la matriz de centros se aplica un modelo de regresión lineal clásico. Supongamos que se aplica un modelo de regresión lineal tomando como variable de respuesta Pulse.
El modelo es: \(Y=43.9379 + 0.1635X_{1}+0.2109X_{2}-1.4132X_{3}+0.2019X_{4}\).
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
Para la variable Syst, se tiene la nube de puntos:
## Syst Diast Art1 Art2
## Min. : 72.5 Min. : 60.00 Min. :2.500 Min. : 3.500
## 1st Qu.: 89.5 1st Qu.: 83.00 1st Qu.:5.000 1st Qu.: 4.500
## Median :107.0 Median : 86.25 Median :5.750 Median : 5.000
## Mean :111.4 Mean : 88.57 Mean :5.864 Mean : 8.977
## 3rd Qu.:129.0 3rd Qu.: 95.00 3rd Qu.:6.500 3rd Qu.: 8.000
## Max. :160.0 Max. :145.00 Max. :9.500 Max. :45.000
## Y.c
## Min. :62.23
## 1st Qu.:67.44
## Median :73.22
## Mean :74.36
## 3rd Qu.:80.91
## Max. :89.70Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
modelo1 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2 , method = "cm")
ypred1 <- sym.predict(modelo1, cardiologicalv2)
#length <- cardiologicalv2[c('Syst')]
length1 <- data.frame(lengthmin=c(90,90,140,110,90,130,60,130,110,138,67,56,78,56,56,90,89,89,78,78,78,90,90,90,140,110,90,130,60,130,110,138,67,56,78,56,56,90,89,89,78,78,78,90),lengthmax=c(100,130,180,142,100,160,100,160,190,180, 89,100,130,89,142,89,160,90,160,89,180,150,100,130,180,142,100,160,100,160,190,180,89,100,130,89,142,89,160,90,160,89,180,150))
clusters1 <- cbind(length1,ypred1$Fitted)
colnames(clusters1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1 <- ggplot() + geom_rect(data = clusters1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf1 <- rectangulos1 +
geom_point(
data = clusters1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 3, alpha = 0.9
)
graf1 
Luego, se calcula el índice de bondad de ajuste geométrico.
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4
9.2 Método de centros y rangos.
Ahora, además de la matriz de centros se crea la matriz de rangos y se estudian los centros más rangos y los centros menos rangos.
Se crea un modelo de regresión lineal clásico con los centros más rangos.
El modelo es \(Y=68.3611 + 0.1158X_{1}+0.1557X_{2}-1.9050X_{3}+0.2077X_{4}\)
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
9.3 Variable Syst.
data.cmasr1 <- cbind(data.cmasr[,-1],Y.cmasr)
ggplot(data.cmasr1, aes(x = Syst, y = Y.cmasr))+geom_point()+labs(title = "Syst vs. Y") #Nube de puntos LENGTH vs Y.cmasr
modelo2 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2, method = "crm")
ypred2 <- sym.predict(modelo2, cardiologicalv2)
clusters2 <- cbind(length1,ypred2$Fitted)
colnames(clusters2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2 <- ggplot() + geom_rect(data = clusters2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf2 <- rectangulos2 +
geom_point(
data = clusters2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4
Se repite lo anterior, pero ahora usando centros menos rangos.
El modelo es \(Y=32.6549+0.1821X_{1}+0.2440X_{2}-2.0934X_{3}+2913X_{4}\)
data.cmenosr1 <- cbind(data.cmenosr[,-1],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = Syst, y = Y.cmenosr))+geom_point()+labs(title = " Syst vs. Y") 
modelo3 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2, method = "crm")
ypred3 <- sym.predict(modelo3, cardiologicalv2)
clusters3 <- cbind(length1,ypred3$Fitted)
colnames(clusters3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3 <- ggplot() + geom_rect(data = clusters3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf3 <- rectangulos3 +
geom_point(data = clusters3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3
## Running with x and y## Index estimation## Estimating R2 Geom for variable = 1## Estimating R2 Geom for variable = 2## Estimating R2 Geom for variable = 3## Estimating R2 Geom for variable = 4
9.3.1 Gráfica final para la variable Syst con el método de centros y rangos.
geom_indicesc <- indice1$results[[1]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[1]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicescmenosr <- indice3$results[[1]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()
geom_indicesc$label <- "centers"
geom_indicescmasr$label <- "centers plus ranges"
geom_indicescmenosr$label <- "centers minus ranges"
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "",
x = "Alpha",
y = "Geom_corr",
color = "Curve"
) +
theme_minimal() +
theme(legend.position = "bottom"))Nota. En los casos en que alpha no cambia, para la curva centros menos rangos se debe utilizar el máximo valor de y, mientras que para la curva centros más rangos, se utilizará centros menos rangos. Todo esto para calcular la integral.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
#ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
#ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
table.diff <- cbind(alpha.vals, diff.geom_corr)
#ggplot(table.diff, aes(x=alpha.vals, diff.geom_corr))+geom_point()
area.acumulada <- cumsum(c(0, diff.geom_corr[-1] * diff(alpha.vals)))
area.acumulada## [1] 0.000000e+00 4.848795e-05 2.657340e-04 1.800041e-03 1.518320e-02
## [6] 2.804019e-02 2.876162e-02 2.930714e-02 2.958858e-02 2.996462e-02
## [11] 3.163963e-02 3.411002e-02 3.595149e-02 4.025150e-02 4.376838e-02
## [16] 5.260108e-02 6.047286e-02 6.895302e-02 8.807972e-02 1.227884e-01
## [21] 1.227884e-01 1.238813e-01 1.508705e-01 1.691103e-01 1.942478e-01
## [26] 2.038283e-01 2.453912e-01 2.709188e-01 2.709188e-01 3.262522e-01
## [31] 4.504013e-01 4.528516e-01 4.578359e-01 4.630234e-01 4.712916e-01
## [36] 4.822705e-01 4.822705e-01 4.855728e-01 4.934812e-01 5.120535e-01
## [41] 5.143865e-01 5.216714e-01 5.338691e-01 5.338691e-01 6.204609e-01
## [46] 7.104424e-01 8.042832e-01 9.567134e-01 1.444200e+00 1.450849e+00
## [51] 1.455554e+00 1.493681e+00 1.514319e+00 1.514319e+00 1.571764e+00
## [56] 1.608208e+00 1.797918e+00 2.485058e+00 3.201757e+00 3.270675e+00
## [61] 3.385113e+00 3.778692e+00 4.232924e+00 4.624609e+00## alpha area
## 1 1.402994 0.000000e+00
## 2 1.800061 4.848795e-05
## 3 2.278057 2.657340e-04
## 4 3.214698 1.800041e-03
## 5 4.525922 1.518320e-02
## 6 5.523881 2.804019e-02
## 7 5.565270 2.876162e-02
## 8 5.601771 2.930714e-02
## 9 5.619691 2.958858e-02
## 10 5.660178 2.996462e-02
## 11 5.748418 3.163963e-02
## 12 5.824925 3.411002e-02
## 13 5.872613 3.595149e-02
## 14 5.955429 4.025150e-02
## 15 6.010835 4.376838e-02
## 16 6.122968 5.260108e-02
## 17 6.220597 6.047286e-02
## 18 6.322232 6.895302e-02
## 19 6.538381 8.807972e-02
## 20 6.904634 1.227884e-01
## 21 6.904634 1.227884e-01
## 22 6.916158 1.238813e-01
## 23 7.250422 1.508705e-01
## 24 7.498996 1.691103e-01
## 25 7.791582 1.942478e-01
## 26 7.902273 2.038283e-01
## 27 8.328997 2.453912e-01
## 28 8.577123 2.709188e-01
## 29 8.577123 2.709188e-01
## 30 9.039883 3.262522e-01
## 31 10.042179 4.504013e-01
## 32 10.062766 4.528516e-01
## 33 10.107478 4.578359e-01
## 34 10.156082 4.630234e-01
## 35 10.237990 4.712916e-01
## 36 10.363750 4.822705e-01
## 37 10.363750 4.822705e-01
## 38 10.403056 4.855728e-01
## 39 10.467604 4.934812e-01
## 40 10.598278 5.120535e-01
## 41 10.614784 5.143865e-01
## 42 10.670498 5.216714e-01
## 43 10.759023 5.338691e-01
## 44 10.759023 5.338691e-01
## 45 11.325317 6.204609e-01
## 46 11.823928 7.104424e-01
## 47 12.311073 8.042832e-01
## 48 13.039666 9.567134e-01
## 49 15.011901 1.444200e+00
## 50 15.038705 1.450849e+00
## 51 15.061173 1.455554e+00
## 52 15.251618 1.493681e+00
## 53 15.357607 1.514319e+00
## 54 15.357607 1.514319e+00
## 55 15.761095 1.571764e+00
## 56 16.007865 1.608208e+00
## 57 17.024864 1.797918e+00
## 58 21.191968 2.485058e+00
## 59 25.450041 3.201757e+00
## 60 25.889604 3.270675e+00
## 61 26.442008 3.385113e+00
## 62 30.509817 3.778692e+00
## 63 35.455139 4.232924e+00
## 64 40.465624 4.624609e+00p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)Probar modelos teóricos, datos de tipo intervalo que sigan cierto tipo de distribución o modelos Doughnout por ejemplo.
Idea: análisis de datos complejos
Idea: bondad de ajuste geométrica para datos de tipo histograma
En 0.7 se intersecan las curvas de pérdida
Buscar un mejor representante en vez del centro, no siempre el centro es el mejor representante.
Workshop PaCMAP.
Combinar PaCMAP con el índice propuesto, separar clusters y buscar el mejor representante por cluster.
El objetivo final es devolver una correlación geométrica en intervalo.
Calcular áreas entre curvas entre mayor es el área entre las curvas entonces más agrupados están los rectángulos (gráficamente uno se puede hacer una idea de la contribución por variable con este valor y con la gráfica de las funciones de pérdida).
Sería importante calcular el valor del área bajo la curva para cada alpha. Hay un alpha ideal que aparece en la función spatgeom.
# Optimización por varianza.
opti.varianza <- function (sym.data, num.dimension)
{
N <- sym.data$N
M <- sym.data$M
num.dimen.aux <- num.dimension
seq.min <- seq(from = 1, by = 2, length.out = M)
seq.max <- seq(from = 2, by = 2, length.out = M)
sym.var.names <- sym.data$sym.var.names
sym.data.vertex <- vertex.interval.new.j(sym.data)
sym.data.vertex.matrix <- sym.data.vertex$vertex
dim.vertex <- dim(sym.data.vertex.matrix)[1]
tot.individuals <- N + dim.vertex
min.interval <- as.vector(as.matrix(sym.data$data[, seq.min]))
max.interval <- as.vector(as.matrix(sym.data$data[, seq.max]))
res.min <- nloptr::lbfgs(min.interval, pca.supplementary.vertex.lambda.fun.j,
lower = min.interval, upper = max.interval, nl.info = FALSE,
control = list(xtol_rel = 1e-08, maxeval = 20000), N = N,
M = M, sym.var.names = sym.var.names, sym.data.vertex.matrix = sym.data.vertex.matrix,
tot.individuals = tot.individuals, num.dimen.aux = num.dimen.aux)
M.x <- matrix(res.min$par, nrow = N)
colnames(M.x) <- sym.var.names
M.x <- scale(M.x)
mean.var <- attr(M.x, "scaled:center")
desv.var <- attr(M.x, "scaled:scale")
sym.data.vertex.matrix.cent <- sym.data.vertex.matrix
for (i in 1:M) {
sym.data.vertex.matrix.cent[, i] <- (sym.data.vertex.matrix.cent[,
i] - mean.var[i])/desv.var[i]
}
M.x <- rbind(M.x, sym.data.vertex.matrix.cent)
pca.max <- PCA(X = M.x, scale.unit = FALSE, ind.sup = (N +
1):tot.individuals, ncp = M, graph = FALSE)
pca.min.sym <- sym.interval.pca.limits.new.j(sym.data, pca.max$ind.sup$coord,
sym.data.vertex$num.vertex)
return(list(Sym.Components = pca.min.sym, pca.min = pca.max,
res.max = res.min))
}# Optimización por distancia.
opti.distance <- function (sym.data)
{
N <- sym.data$N
M <- sym.data$M
seq.min <- seq(from = 1, by = 2, length.out = M)
seq.max <- seq(from = 2, by = 2, length.out = M)
sym.var.names <- sym.data$sym.var.names
sym.data.vertex <- vertex.interval.new.j(sym.data)
sym.data.vertex.matrix <- sym.data.vertex$vertex
dim.vertex <- dim(sym.data.vertex.matrix)[1]
tot.individuals <- N + dim.vertex
min.interval <- as.vector(as.matrix(sym.data$data[, seq.min]))
max.interval <- as.vector(as.matrix(sym.data$data[, seq.max]))
init.point <- as.vector(as.matrix(centers.interval.j(sym.data)$centers))
res.min <- nloptr::lbfgs(init.point, pca.supplementary.vertex.fun.j,
lower = min.interval, upper = max.interval, nl.info = FALSE,
control = list(xtol_rel = 1e-08, maxeval = 20000), N = N,
M = M, sym.var.names = sym.var.names, sym.data.vertex.matrix = sym.data.vertex.matrix,
tot.individuals = tot.individuals)
M.x <- matrix(res.min$par, nrow = N)
colnames(M.x) <- sym.var.names
M.x <- scale(M.x)
mean.var <- attr(M.x, "scaled:center")
desv.var <- attr(M.x, "scaled:scale")
sym.data.vertex.matrix.cent <- sym.data.vertex.matrix
for (i in 1:M) {
sym.data.vertex.matrix.cent[, i] <- (sym.data.vertex.matrix.cent[,
i] - mean.var[i])/desv.var[i]
}
M.x <- rbind(M.x, sym.data.vertex.matrix.cent)
pca.min <- FactoMineR::PCA(X = M.x, scale.unit = FALSE,
ind.sup = (N + 1):tot.individuals, ncp = M, graph = FALSE)
pca.min.sym <- sym.interval.pca.limits.new.j(sym.data, pca.min$ind.sup$coord,
sym.data.vertex$num.vertex)
return(list(Sym.Components = pca.min.sym, pca.min = pca.min,
res.min = res.min))
}9.4 Primer intento, Método Best Point.
Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo abalone de RSDA. Se obtiene la matriz de vértices asociada.
library(RSDA)
datos <- abalone
#Número de vértices de la tabla abalone:
nv <- (2^{dim(datos)[2]})*dim(datos)[1] #3072
#RSDA:::sym.umap.symbolic_tbl()
#RSDA:::expand_rows
vertex <- function(df){
l <- lapply(seq_len(ncol(df)), function(x) list(1, 2))
df_i <- expand.grid(l)
funs <- list(min, max)
funs <- lapply(df_i, function(i) funs[unlist(i)])
out <- lapply(seq_len(nrow(df)), function(i) {
fila <- df[i, ]
out <- lapply(seq_along(funs), function(i) {
unlist(lapply(funs[[i]], function(.f) .f(fila[[i]])))
})
out <- as.data.frame(do.call(cbind.data.frame, out))
colnames(out) <- colnames(df)
return(out)
})
out <- as.data.frame(do.call(rbind.data.frame, out))
colnames(out) <- colnames(df)
return(out)
} #Esta es la funcióne expand_rows del código base de sym.umap
datos.v <- vertex(datos)
datos.v <- round(datos.v, 2)
#Qué pasa si aplico un modelo de regresión para los vérticesmodelo.vertices <- lm(WHOLE_WEIGHT ~., datos.v)
Y.v <- modelo.vertices$fitted.values
Y.v <- round(Y.c,2)Para la variable LENGTH, se tiene la nube de puntos: